Most Importantly, No Reddit

Most Importantly, No Reddit On Friday evening, I made the disturbing discovery that my computer’s power adapter was dead. A long time coming, it had been on the fritz for about three weeks â€" I’d plug it in, but the battery wouldn’t begin to charge until I gave the plug a little jiggle. The odd thing was that I was just using the plug not five minutes earlier. I then unplugged the laptop, took it to another room, and then came back. I’m not sure what happened during those five minutes, but not even a jiggle could resuscitate its powerful abilities (pun intended). After fruitlessly trying to get the thing to work, I quickly ordered a new adapter online the following day. It was scheduled to arrive Monday, and while I knew I would miss my computer the whole weekend, I was ready to take advantage of this weekend off to get some serious work done. No YouTube, no Grooveshark, and, most importantly, no Reddit. This weekend, I said to myself, was bound to be my most productive all semester and perhaps ever. How navØve. I was able to complete my Spanish homework without issue â€" my textbook and two workbooks were all I needed. I now feel moderately prepared for tomorrow’s exam, and I should be fully prepared once I finish this post and get back to studying. However, when it came to just about everything else, well no, it was far from the most productive weekend of the term. I tried to work on my UROP, which involves computing statistics about traffic in a section of Singapore. I had been really guilty about not devoting enough time to the project as I would like, and this weekend â€" I had vowed earlier â€" I’d really knuckle down and work on it. But it required MATLAB. And previous data I had already spent time computing. And that was on my computer. So, sorry, Swapnil, it’ll have to wait a bit longer. At the same time, I came to the alarming realization that my first set of graduate applications is due in mid-December. Mid-December! I have plenty of time to work on them, of course, but the three people whom I would like to ask for recommendations? Well, unlike me, they may not be so willing to pull all-nighters to get something in before an application deadline (did that last week for externships). They, as Matt put it, have lives too, and I needed to give them ample time. (Note, for the record, that I absolutely will not be pulling all-nighters to get my college applications in, and neither should you. Im just saying that if I had to, due to unforeseen circumstances, I would.) Two of the three people who I decided to ask recommendations from are overseas and so I needed to ask them via e-mail. There were e-mail addresses, background information, resumes, etc, that I wanted to have access to as I prepared said e-mails. And, guess where those were? Yes, so, I didn’t get around to that until today. I needed to also pay some credit card bills. But, Im not doing that from a public computer, nor am I searching through thousands upon thousands of e-mails in Webmail (can you tell I dont use Gmail?) looking for that esoteric username they assigned me. No, still havent done that yet. Now, now, I know what you’re thinking: (1) Use an Athena computer. Yes, I did, but I had more pressing things than work, silly. (2) This is why you should back things up. Don’t worry; I have learned that lesson by now. My computer crashed suddenly in September of my sophomore year, and I was practically crying all the way to the post office as I mailed off my fallen hard drive â€" and a $250 check â€" to recover the hundreds of photos taken during the second half of my summer that I had foolishly neglected to back up. (Ah, I’ll just get around to it tomorrow, I kept saying.) A year and a half later, earlier this year, when my computer was stolen on an overnight train in Eastern Europe (another long, sad, but easily predictable story), I had at least some solace in the fact that I had backed up everything, especially my precious pictures, just two weeks earlier (and not emptied my camera’s memory card like I had planned). But, there’s something exhausting about trolling through and unzipping all those backup files. Instead, I sought to go the easier route â€" borrowing a power adapter from a fellow Baker resident. I e-mailed out to the dorm mailing list, but, unfortunately, there wasnt a single person that could help out. Perhaps this is just a testament to how many people have Macs (yes, Im willing to admit it now; I sometimes have Mac envy). Or maybe it was a testament to how many plugs HP makes (so many that when they offered to replace one for free a couple years ago, they sent me the wrong one: oh, your computer has an Intel processor, so you needed the 90-watt one; sorry about that!). But, no, its neither; its just a testament to the fact that nobody likes me. So, yes, with no help from fellow Bakerites, I had to suffer the whole weekend without my computer, but with a wonderful â€" albeit not airtight â€" excuse for putting off so much work. But to think my parents had to go decades living like that wow makes me shudder.

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Dr. King s Letter From Birmingham Jail - 1342 Words

Dr. King Lays the Clergymen’s Anxiety to Rest Dr. Martin Luther King addressed many topics in, â€Å"Letter from Birmingham Jail†. He answered all the issues that were aimed towards him in a very skillful and well thought out manner. These issues came from, â€Å"A Call For Unity†, which was a letter that was published by eight local clergymen expressing their feelings about what Dr. King was doing. One concern in particular that King did an outstanding job of confronting was that of the clergymen’s anxiety about him breaking the law. King addresses the question of, â€Å"How can you advocate breaking some laws and obeying others?† by clarifying that there are just and unjust laws. He also goes on to explain the difference between the two, the effect of unjust laws on the people that they are aimed towards, as well as examples of such laws. Furthermore, he explains why they should be broken and gives examples of when they’ve been broken in the past with the usage of civil disobedience. First, Dr. King clears up any idea that he’s just someone who has broken the law for no reason. He does this by saying; â€Å"I would be the first to advocate obeying just laws. One has not only a legal but a moral responsibility to obey just laws. Conversely, one has a moral responsibility to disobey unjust laws.† (Para 15) This statement tells us that Dr. King is simply adhering to his moral responsibility by doing as he’s supposed to. He knows that following a law that is not fair makes no sense, and itShow MoreRelatedDr. King s Letter From Birmingham Jail1667 Words   |  7 Pagesyear of 1963, when racial discrimination was evident in the community, Dr. King delivered two of his most noted works called the â€Å"I have a Dream† speech and â€Å"Letter from Birmingham Jail† to the public. These two pieces, quickly following each other in succession, were literary works of Dr. King devoted to the cause of racial equality and used eclectic devices and a ppeals to achieve that goal. King’s purpose bolstered in his â€Å"Letter† and â€Å"Dream† speech by key rhetorical devices are supported by audienceRead MoreDr. Martin Luther King s Letter From Birmingham Jail1428 Words   |  6 PagesOn April 16, 1963, Dr. Martin Luther King, Jr. wrote what has become known as the â€Å"Letter from Birmingham Jail.† A long document, it was addressed to Birmingham’s local clergymen because they had been critical of his work and ideas. Dr. King believed their criticism was in good faith, and pointed out that he was in Birmingham because he had been invited by the local affiliate of the Southern Christian Leadership Conference, showing the religious commonalities between himself and the clergymen. HoweverRead MoreAntigone And Dr. Martin Luther King Jr. s Letter From Birmingham Jail1233 Words   |  5 PagesIn Sophocles’ Antigone and Dr. Martin Luther King, Jr.’s â€Å"Letter from Birmingham Jailâ⠂¬ , Antigone and Dr. Martin Luther King, Jr. used resistance against powerful leaders to follow their morals and make a statement. Dr. Martin Luther King, Jr.’s approach towards the reconstruction of society’s cultural understanding of segregation used civil disobedience in a more public and large-scale approach, whereas Antigone’s use of civil disobedience defied the law in a much more private, small-scale way toRead More Dr. Martin Luther King Jr.s Letter From a Birmingham Jail Essays1088 Words   |  5 PagesDr. Martin Luther King Jr.s â€Å"Letter From a Birmingham Jail† In King’s essay, â€Å"Letter From Birmingham Jail†, King brilliantly employs the use of several rhetorical strategies that are pivotal in successfully influencing critics of his philosophical views on civil disobedience. King’s eloquent appeal to the logical, emotional, and most notably, moral and spiritual side of his audience, serves to make â€Å"Letter From Birmingham Jail† one of the most moving and persuasive literary pieces of the 20thRead Moreâ€Å"a Comparison of Dr. Martin Luther King, Jr.’S ‘I Have a Dream’ Speech and ‘Letter from a Birmingham Jail’†.1444 Words   |  6 Pagesâ€Å"A Comparison of Dr. Martin Luther King, Jr.’s ‘I Have a Dream’ speech and ‘Letter from a Birmingham Jail’†. 9% Similarity Born in Atlanta Georgia in 1929, Dr. Martin Luther King Jr., conceivably lived as one of the greatest social and religious leaders in a country where a group of its citizens had to endure excruciating conditions of disenfranchisement, inferiority and degradation of a second class citizenship by reasons of race, color or origin. In effort to condemn allRead MoreAn Analysis of Letter from a Birmingham Jail Essay1090 Words   |  5 Pages Letter from a Birmingham Jail was written by Doctor Martin Luther King Jr. in April of 1963, as he sat, as the title states, in a Birmingham, Alabama jail. King had been jailed for his participation in a peaceful protest of segregation in public places such as lunch counters and public restrooms (Berkley, 2003). While jailed, King read a criticism of the protest by a group of white ministers, who felt such demonstrations â€Å"directed and in part led by outsiders† were â€Å"unwise and untimely†Read MoreRhetorical Analysis Of Martin Luther King Jr.976 Words   |  4 PagesMartin Luther King Jr. wrote numerous speeches in efforts to inspire the idea of non-violent protesting in hopes of eventually reaching racial equality. Under what conditions can a man with seemingly no connection to a local community step in and assume the mantle of leadership as a spokesman for a segment of that community’s population? In all of the speeches, one way or another , Dr. King used several different rhetorical devices in order to defend his own actions. In specific, two of his speechesRead MoreLetter From Birmingham Jail Analysis1617 Words   |  7 Pages1960’s faced solely due to the melanin in their skin (King 2). Among these African Americans was the reverend, doctor, humanist, husband, and Civil Rights activist, Mr. Martin Luther King, Jr. Dr. King was a middle class, black man with a life-long devotion of implementing ethnic equality to African Americans nationwide. Following one of Rev. King’s peaceful protests in Birmingham, Alabama, he was jailed on accounts of â€Å"parading without a permit† (King 3). While in jail, Martin Luther King, JrRead MoreLetter From A Birmingham Jail972 Words   |  4 PagesRhetorical Analysis: Letter from a Birmingham Jail Racism is part of America’s history. Historical leaders like Martin Luther King, Jr. brought the Injustice problems to the light. King, Jr. â€Å"Letters from a Birmingham Jail confronts racism in the United States of America through his response letter to the clergymen criticism, while he is in jail due to holding a protest in Birmingham, Alabama. King, Jr. wrote â€Å"Letter from a Birmingham Jail† to defend the non-violent protest. He claims that the protestRead MoreMartin Luther King Jr : Letter From Birmingham Jail Essay1678 Words   |  7 Pages Martin Luther King Jr: Letter from Birmingham Jail Hao Ran Hu SUNY Broome Hao Ran Hu Global History Professor St.Clair 2016 Martin Luther King Jr: Letter from Birmingham Jail One of the interesting Documents in World History is the ‘Letter from Birmingham Jail’ by Martin Luther King Jr who was born as Michael King in 1929 in Atlanta. His parents were part of

Distillation Experiment Free Essays

SUMMARY The aim is to observe distillation process of ethanol-water solution and to measure the alcohol content after process in this experiment. 500 ml of solution with an alcohol content of 32% (v/v) is used for this experiment. Temperature values are recorded for every 10 ml alcohol obtained in the flask. We will write a custom essay sample on Distillation Experiment or any similar topic only for you Order Now The process is repeated in our experiment and for the first process, the data collection process continues until the distillate reaches to 200 ml. The concentration of alcohol is measured for first process by hydrometer. For the second process, approximately 200 ml of distillate containing 70% alcohol is used and data collection continues until the distillate reaches 150 ml. Finally, the concentration of alcohol is also measured after 2nd process as 82%. INTRODUCTION The objective of this experiment is to distillate the alcohol-water solution into ethanol and water. Distillation is a process of separating mixtures based on differences in volatilities of components in a boiling liquid mixture. Distillation is a unit operation, or a physical separation process, and not a chemical reaction. The basic requirement of distillation is that the components of the liquid solution must have different boiling points. There are some types of distillation methods which are flash distillation, simple batch distillation, simple steam distillation, continuous distillation, vacuum distillation, etc. : Flash distillation It is a single stage process which liquid mixture is vaporized. The vapor and the liquid are come to equilibrium, and these phases are separated. Simple steam distillation This is a separation process at lower temperatures. This process is often used to separate a high boiling component from small amounts of nonvolatile impurities. Continuous distillation This is a process in which a liquid mixture is continuously fed into the process and separated fractions are removed continuously. Vacuum distillation It is used for some compounds having very high boiling points. Instead of the increasing the temperature too much, lowering the pressure is preferred in this distillation type. In this experiment we used simple batch distillation in order to distillate alcohol-water mixture. Simple batch distillation This is a separation process which the liquid charge is boiled slowly and the vapors are withdrawn as quickly as vapors form to condenser, where the distillate, condensed vapor, is collected. The first portion of vapor condensed will be the richest in the more volatile component. Vapor-liquid equilibria take an important role in distillation process. Vapor-Liquid-Equilibria (VLE) Constant pressure VLE data is obtained from boiling point diagrams. VLE data of binary mixtures is often presented as a plot, as shown in the figure below. The curved line is called the equilibrium line and describes the compositions of the liquid and vapour in equilibrium at some fixed pressure. Distillation experiment is applied to two miscible liquids which are ethanol-water, soluble in each other in all ratios. Mixtures of ethanol and water form an azeotrope. Azeotropic mixture: Azeotropic mixture is a solution that forms a vapor with the same concentration as the solution, distilling without a change in concentration. The composition of the liquid phase at the boiling point is identical to hat of the vapor in equilibrium with it, and azeotropes form constant-boiling solutions. The exact composition of the azeotrope changes if the boiling point is altered by a change in the external pressure. Ethyl alcohol and water form an azeotrope of 95. 6% at 78. 1 Â °C. Azeotropic systems give rise to VLE plots where the equilibrium curves crosses the diagonals. METHODS AND MATERIALS -Distillation apparatus -Alcoholmeter -Graduated cylinder -5 00 ml of 30% (v/v) water-ethanol mixture Source: Retrieved from http://www. baruch. cuny. edu/wsas/academics/natural_science/chm_1000/6_wine. df The distillation apparatus is for the separation of two miscible liquids by taking advantage of their boiling point differences. The mixture is put in the distillation flask, and a thermometer is located in there. The heater has a knob that is used to adjust the heating. Cold tap water is circulated in the condenser to condense the vapor. First, the ethanol – water mixture was poured into the distillation flask, and boiling chips were used to prevent over bubbling. Then the heater was turned on at a moderate level to prevent fast heating and better separation of the liquids. After the first drop of the distillate was obtained, the temperature was recorded. Every 10 milliliters, the temperature in the flask was recorded. At the end of the distillation, an alcoholmeter was used to measure the alcohol content of the distillate. 200 milliliters of distillate was distillated again in the same manner to obtain a higher alcohol percentage in the final product. DATA CALCULATION Notations used: A: Ethanol B: Water XA ? Mole fraction of ethanol in liquid YA ? Mole fraction of ethanol in vapor XB? Mole fraction of water in liquid YB ? Mole fraction of water in vapor Assumptions: – Pressure is 101,32kPa – Constant physical properties – Condensed fluid drops on the wall of still are neglected Initial data: – 500 mL of ethanol-water mixture is used for the first distillation. – 200 mL of ethanol-water mixture is used for the second distillation. Calculation: XA YA values can be calculated from the Raoult’s law equation; ? A + ? B = P PA* XA + PB* XB = P ? Since XA + XB = 1 PA* XA + PB* (1- XA)= P XA = (P – PB)/( PA – PB) The PA PB values were obtained according to the temperature data. (Acland,T. 2011) 1st DISTILLATION: T(? C)PBPAXAYAXBYB 7843,5100,11,0015551,0032540,000,00 78,544,4102,10,9864820,9940760,0135180,005924 7945,3104,10,9527210,9788620,0472790,021138 79,245,7104,90,9395270,9727240,0604730,027276 79,345,9105,30,9329970,9696460,0670030,030354 79,546,3106,20,9185310,9627710,0814690,037229 8047,2108,30,8857610,9467820,1142390,053218 80,548,2110,40,8540 190,9305540,1459810,069446 8149,2112,60,8220820,9136050,1779180,086395 81,550,2114,80,7913310,8966130,2086690,103387 8251,21170,7617020,8795810,2382980,120419 82,552,2119,30,7320420,8619480,2679580,138052 353,3121,60,7030750,8438010,2969250,156199 8455,4126,30,6476730,8073540,3523270,192646 8557,7131,20,5934690,7684880,4065310,231512 85,558,8133,70,567690,7491140,432310,250886 8762,4141,50,4920350,687160,5079650,31284 8864,8146,90,4448230,6449320,5551770,355068 88,566,1149,60,4217960,6227870,5782040,377213 9070158,10,3555050,5547310,6444950,445269 The average composition of total material distilled, Yav was measured by using hydrometer as 70%. So the final composition of remaining liquid,X2, can be obtained by material balance using Rayleigh equation: L1X1 = L2X2+ (L1 – L2)Yav 00(0,32) = 300 X2 + 200(0,7) ? X2 = 0,067 That means, 6,7 % of ethanol remained in the distillation still. 2nd DISTILLATION: T(? C)PBPAXAYAXBYB 78,544,4102,10,9864820,9940760,0135180,005924 79,546,3106, 20,9185310,9627710,0814690,037229 8047,2108,30,8857610,9467820,1142390,053218 8149,2112,60,8220820,9136050,1779180,086395 8251,21170,7617020,8795810,2382980,120419 8455,4126,30,6476730,8073540,3523270,192646 8864,8146,90,4448230,6449320,5551770,355068 9070158,10,3555050,5547310,6444950,445269 The average composition of total material distilled, Yav was measured by using hydrometer as 82%. So the final composition of remaining liquid,X2, can be obtained by material balance using Rayleigh equation: L1X1 = L2X2+ (L1 – L2)Yav 200(0,7) = 50 X2 + 150(0,82) ? X2 = 0,34 That means, 34 % of ethanol remained in the distillation still. DISCUSSION In first distillation, according to data obtained boiling point diagram is drawn. This graph can be seen as incomplete because some data is missing in order to complete graph since high temperature is not reached. Moreover, azeotropic point cannot be seen because we are not able to change pressure, so we cannot see that point and forward. In boiling point diagram graph for second distillation, we omit some of data because fraction is found negative, which is not possible. There may be error due to experimental condition or reflux. CONCLUSION In this experiment, our aim is to learn basic distillation concept and how to take and evaluate our data. We also learnt how to put data into boiling point diagram. In first distillation it is obtained 70% alcohol water solution and in the second distillation it is obtained 78% alcohol water solution. However, because of negative fraction values, we are not able to put all the data into boiling point diagram. REFERENCES Ackland, T. (2011). Home distillation of alcohol. Retrieved from http://homedistiller. org/ Geankoplis, C. J. (2003). Transport processes and separation process principles. Prentice Hall. Seperation Process. Distillation. Retrieved from http://www. separationprocesses. com/ Distillation/DT_Chp05. htm Wikipedia. Distillation. Retrieved from http://en. wikipedia. org/wiki/Distillation Wikipedia. Azeotropic Distillation. Retrieved from http://en. wikipedia. org/wiki/ How to cite Distillation Experiment, Essay examples

Separate Peace Responsibility Essays - Phillips Exeter Academy

Separate Peace: Responsibility A Separate Peace: Responsibility A responsibility is something for which one is held accountable. Often people say that one is responsible for ones own words and actions; if something happens as a result of something one does one is responsible for it. But is it possible that something could be the result of various actions from different people who are therefore equally responsible, or is there always one person who is most responsible for the incident at hand? Such a situation where this question is relevant is present in the novel A Separate Peace by John Knowles. In the novel, the main character, Gene, ponders his responsibility for the death of his best friend, Phineas or Finny. After reading Genes account of the events that led to Finnys death the reader may observe that there are three people who are all partially at fault for Finnys death. Gene, a classmate named Brinker, and Phineas all had something to do with the incident, but who was most responsible for it? Gene is probably the most obvious to blame for part of Phineas death. Gene clearly feels guilty, that is why he returns to the tree fifteen years after the fact, for some sort of closure. As Gene and Finny were about to jump from a tree branch into the river together, Gene shook the branch causing Phineas to fall into the river unexpectedly and hurt his leg. Later on, when Phineas re-injured his leg and was having it set in a routine operation, he passed away. The doctor said that it was probably because some marrow entered his blood stream and caused his heart to stop. But if Finny had never fallen in the first place he would have not been on that operating table. Therefore, indirectly an action of Genes eventually resulted in Finnys death. But was this action done consciously? The author does not specify. My knees were bent and I jounced the limb(Knowles p.52) says Gene in his account of the incident. I jounced is an active verb but were bent is passive meaning that some unknown fo rce bent Genes knees and as a result of that he jounced the limb. Since this action was not totally Genes he is not thus totally responsible for the fall or the events that occurred as a result of it. Brinker, Gene and Finnys classmate was responsible for the circumstances that lead to Phineas second fall. Brinker suspected that Gene was responsible for Finnys first fall and begrudged him somewhat for not enlisting in the army with him when he had wanted to. It was Brinker who called together the trial in which Gene was prosecuted for purposely causing Finny to fall off the tree. But even if Gene was to blame for Finnys first fall, it was not necessary to drag Finny out of bed in the middle of the night and put him through such emotional turmoil when he was still physically vulnerable from the accident. If Brinker had not organized the trial Finny would have never rushed out in such an upset manner causing him to fall and hurt himself again. The doctor was not sure why Phineas died. In the middle of it [the surgery] his heart just stopped. I cant explain it.(Knowles p.185) He said. Later on the doctor conjectured that Phineas probably died when marrow entered his blood circulation and clogged his heart but Gene meant the world to Finny. The idea Brinker introduced to Phineas that his best friend would betray him hurt Phineas severely and maybe even caused him to loose the will to live. Brinkers actions were crucial to Finnys death and since they were done with cruel intentions Brinker is largely responsible for the death of his classmate. Surprisingly enough Finny is partly responsible for his own death. He knew that jumping off the tree into the river was dangerous hence the name of the club Super Suicide Society of the Summer Session(Knowles p.24) whose membership requirement was one jump from the tree. Also, if not for Finny Gene wouldnt even have come to the meeting the night of the accident, Gene wanted to stay in the dorm and study but Finny used reverse

Women Liberation during the Socialist Era

Women Liberation during the Socialist Era Introduction This lecture is a close examination of women liberation during the Cultural Revolution in China. Despite the great suppression that women were subjected to, they stood up against all odds to defend their rights. Rising from the lows of an abused slave, Wu Qiong Hua showed a great spirit of a soldier.Advertising We will write a custom research paper sample on Women Liberation during the Socialist Era specifically for you for only $16.05 $11/page Learn More She had a strong will to stand up for her rights and that will led her into joining the army and finally became an army leader. She had a great personality and great determination to fight for what was right. Considering the male dominated society and era that Wu Qiong Hua lived in, it is hard to imagine the feat she was able to accomplish. She was more than a fighter; she had the personality to fight women suppression. Thesis Women in China had been chained up by the traditional feminine role for thousands of years. They were coerced to obey the three obedience and four virtues. Mao introduced a new perspective of viewing women thus redefining the woman theory in a more liberal perspective. This was during the Cultural Revolution and women gracefully enjoyed a new status they had never experienced before. The new era in womanhood witnessed deep transformations spanning from the external appearance to the internal perceptions which had been deep seated during the class struggle era. The woman soldier is squarely a product of the actions of Mao, and thus of the socialist China. She is a witness and a proof of the transformation that took place during the socialist era. Women of this era were the contradictory mixture. They were the modifiers and were also the ones that were modified. The Red Detachment of Women, both in 1961 film version and 1964 ballet version, presented the enormous transformation of the female figure and their social status during the era of socialist C hina. The Red Detachment of Women, which had been assumed as the â€Å"model work† in Cultural Revolution, also reflects the life, politic, ideology and social values at the time.Advertising Looking for research paper on history? Let's see if we can help you! Get your first paper with 15% OFF Learn More Historical Background The pre-socialist era was oppressive towards women. There were very many oppressive practices that the society embraced and which greatly burdened women. Fulton discusses these practices in great details. The first practice she highlights is that of foot-binding. This is an eleventh century practice introduced to the society by the wealthy class. Foot binding was very painful, but unfortunately very significant because it determined whether a woman could get married or not. This practice started at a very tender age of three years (Fulton 35). Another way that women were oppressed was in the manner in which the society allowed men to relate to them. Wives were treated with a lot off disrespect. A wife was a subject to the family she was married to. She did not have any powers but always had to be submissive to the family of her husband. Women also fostered oppression against themselves. A first wife had more power than the other wives and using this power she could cruelly treat the other wives. Concubines were used by men for sexual pleasure as well as for children siring. Wives had more power than concubines and as result concubines were also cruelly treated by wives. If a wife was barren she could take the children of a concubine. If a husband died, his wife took charge of the concubines and would do anything with them including selling them to a brothel. Prostitution was even worse. There were times when peasants resorted to sell their girls to prostitution (Fulton 35). On the question of women liberation from the above snapshot, Mao did a revolutionary work. Laws were instituted that gave protection to w omen, and consequently gave then a leeway from oppression. One such law was the right to get a divorce.Advertising We will write a custom research paper sample on Women Liberation during the Socialist Era specifically for you for only $16.05 $11/page Learn More A wife could request for a divorce from her husband. This gave a great chance for wives to divorce husbands who abused them. Foot binding was also becoming a past act by 1949 as result of intentional advances by Mao to liberate women. Arranged marriages were banned – men and women had to choose each other for marriage. This gave great freedom to women to settle into marriage with men they were comfortable with. Marriage contracts and associated sales were also banned. This gave some dignity to women not to be viewed as goods for sale. Prostitution was outlawed and concubines were freed. A federation was started, Women’s Federation, to better the status of women in the society. Women wer e encouraged to join schools and the workforce (Fulton 35). Analysis of the scenes in film and ballet version Both the film and ballet version of The Red Detachment of Women reflects the status of women during the pre-socialist era. Wu Qiong Hua best illustrates this as she moves from being a slave into being a woman soldier. At the start of the film and the ballet, we get introduced to a slave girl who has been trying to escape from abuse in vain. She is subjected to beatings and torture every time she tries to escape. It seems she cannot do anything to free herself. The implication that is shed as at this level is that women were oppressed by forces above them and which they could not control (Xie 1). This was a true depiction of the events of the time because women were always under the control of their husbands and their mothers in law and if they were not married they were under their fathers’ and mothers’ control. As already discussed above, there was a time when families could sell their girls to get cash for food. Fulton also notes that at this time, food was so scarce that parents had to choose among the children who was to eat and who to starve and more often than not girls were forced to go hungry (Fulton 36).Advertising Looking for research paper on history? Let's see if we can help you! Get your first paper with 15% OFF Learn More The statement is simple, girls/women had nowhere to escape to for freedom whether they were married or not; oppression was right on their necks. This is exactly what is depicted at the opening moments of the film and ballet versions (Xie 1). It is worth noting that it is only the initial moments of the film and ballet versions that represent the status of women in the pre-socialist era. The depiction is that women were completely hopeless and they had nowhere to run. When Changqing gets attracted to the situation of Wu Qiong Hua, this marks the beginning of the desire by the Communist Party to liberate women and the whole of China indeed from oppression. The director used music and light to show the situation between good (socialist era) and bad (pre-socialist era). Changqing represents the good side which is bent on helping Wu Qiong Hua from the oppressive side Nan Batian (Xie 1). Gender norms at the time During the socialist era, women experienced great changes in their societal s tatus. One change which greatly changed the position of women in the society was the increase in their duties and especially the things they could do. Women were allowed to join the labor force in the factories. They learned how to run the factories. They were also allowed to go to school and gain academic competency. The call for education was even among the peasants and thus generally women gained education, and consequently were more informed. Education and empowerment from gains earned by joining the workforce raised women to a new level confidence; women gained some sort of independence which gave them some self-confidence. With this sort of confidence and the backup of the law, women were empowered to bargain even at the household level (Fulton 37). The role of the Women’s Federation cannot be assumed. This organization worked hard to see that women were given an opportunity to progress in the society. Some of the functions that the federation undertook was closing down of brothels and ensuring that all concubines were freed. The federation organized for the employment of women and did all it could to ensure that those who wanted to join school did that. Women were also informed of their rights concerning the various issues which touched their lives such as being married against their wish (Fulton 37). The empowerment of women did one great thing – it reduced the gender gap which had existed before. Women were no longer viewed as doormats but were accorded some respect. The mixture of women and men in the workplace made it possible for the notion of male gender superiority to melt. This era therefore uplifted the female gender, and as a result helped to wither masculinity dominance in the society. In other words, this time helped greatly in fostering equality. There was a great change in ideology on the role of women in the society. The society was turned round to respect and support women whom they had so much scorned. Women and Masculinit y Despite the stated above facts that the status of women changed under the socialist era, some critics have observed that the change in gender roles and the uplifting of women status was not as high as it has been said to be. According to Evans, women still played the roles of taking care of their families especially children. She argues that the fact that women were allowed to enter the workforce did not mean they neglected their primary role of taking care of their children, husbands and often parents-in-law. This was their customary domestic division of tasks (Evans 1). It is further noted that there was a violation of very basic issues that relate to women. The manner in which they were integrated into the workforce left much to be desired. The phrase â€Å"Whatever men can do, women can do too† was popularized in China at this time. Unfortunately, this led to rendering women masculine. Women were pushed into being like men – some sources refer to women of this ag e as ‘iron girls’ (Wang 136). For instance, they to wear the same uniforms as men and they made to appear as men. Men were being used as the yardstick for evaluating women (Li 1). This meant that women were losing their womanhood and were being transformed to be like me. This was degrading to women. Women soldiers under political influence As already noted above, women gained from the recognition they received from the political sector during the socialist era. It has been noted that the Communist Party had the interest of liberating women way before it was in power. This desire started among the founders of the party before it was even formed. As time progressed, much development unfolded and led to including women in the movement of the party after it was formed. Women issues were discussed in the first, second and third congress of the party back in 1923 (Evans 1). When the communist Party ascended to power, it had a clear picture of the need to liberate women. This is because women liberation was an issue which had been discussed at length way from the very beginning of the formation of the party. However, Evans argues that women liberation and politics, especially party politics, have been mixed up in issues to do with the definition of some terms. It has further been argued that depending on a term picked, the definition and perspective of liberation would take a different course. It is noted that the term given to liberation of women could change in definition depending on the party priorities (Xie, Lily, and Barry 1). Conclusion To conclude this lecture, we must note that the study of Chinese women warriors is very important. This is because they have made an important contribution in history of China. They stood up against barbaric traditions and fought their way to freedom. They therefore made a great contribution to the progress of the reformation of China. Asian women warriors in general have also made great contribution to their speci fic homelands in ensuring women rights are uplifted. The studies of women warriors in general therefore help us to appreciate the vital role that women play in the society to ensure that all society members are treated equally. Evans, Harriet. â€Å"The Language of Liberation: Gender and Jiefang in early Chinese Communist Party.† Intersections: Gender, History and Culture in the Asian Context 1 (1998): 1. Print. Fulton, Jessica. Holding up Half the Heavens: The Effect of Communist Rule on China’s Women. Class Article, 2013. Print. Li, Yuhui. â€Å"Women’s Movement and Change of Women’s Status in China.† Bridge, 2013. Web. https://vc.bridgew.edu/jiws/ Wang, Zheng. Maoism, Feminism, and the UN Conference On Women: Womens Studies Research In Contemporary China. Journal of Womens History 8.4 (1997): 126. Print. Xie, Bingying, Lily C. Brissman, and Barry Brissman. A Woman Soldiers Own Story: The Autobiography of Xie Bingying. New York: Columbia Univers ity Press, 2001. Print. Xie, Jin. The Red Detachment of Women. Shanghai Tianma Film Studio production, 1961. Film.

Inequalities on ACT Math Strategies and Practice

Inequalities on ACT Math Strategies and Practice SAT / ACT Prep Online Guides and Tips Inequality questions come in a variety of shapes and forms on the ACT, but, no matter their form, you will see approximately three inequality questions on any given test. This means that inequality questions make up 5% of your overall ACT math test. Now, 5% of your test might not sound like a lot, but with only a quick brush-up on inequalities, that's an additional 5% of your questions that you're bound to rock! This will be your complete guide to inequalities on the ACT: what they are, the different types of ACT math problems on inequalities, and how to solve them. What Are Inequalities? An inequality is a representation that two values are not equal or that two values are possibly not equal. There are different types of inequalities and different symbols to denote these different relationships. ≠  is the "unequal" sign. Whenever you see this sign, you know that two values are not equal, but nothing more. We don't know which value is greater or less than, just that they are not the same. If we have $y ≠  x$, we do not know if $y$ is greater or less than $x$, just that they do not equal one another. is the "greater than" sign. Whichever number or variable is facing the opening of the sign is always the larger of the two values. (Some of you may have learned that the sign is a "crocodile" and that the crocodile always wants to eat the larger value). For instance, $x 14$ means that $x$ can be anything larger than 14 (it can even be 14.00000000001), but it cannot be 14 and it cannot be less than 14. is the "less than" sign. Whichever number is facing away from the opening of the sign is the lesser of the two values. This is just the greater than sign in reverse. So $14 x$ is the exact same equation we had earlier. $x$ must be larger than 14, 14 must be smaller than $x$. ≠¥ is the "greater than or equal to" sign. This acts exactly the same as the greater sign except for the fact that our values can also be equal. Whereas $x 14$ meant that $x$ could only be any number larger than 14, $x ≠¥ 14$ means that $x$ could be equal to 14 or could be any number larger than 14. ≠¤ is the "less than or equal to" sign. Just as the less than sign acted as a counter to the greater than sign, the less than or equal to sign acts counter to the greater than or equal to sign. So $x ≠¥ 14$ is the exact same thing as saying $14 ≠¤ x$. Either way, we are saying that 14 is less than or equal to $x$, $x$ is greater than or equal to 14. Each symbol describes the relationship between two values, but we can also link multiple values in a string. For instance, we can say: $5 x 15$ This gives us both an upper and a lower limit on our $x$ value, because we know it must be both larger than five and less than 15. If we only had $5 x$, the upper limit of $x$ would stretch into infinity, and the same with the lower limit if we only had $x 15$. For tips on how to keep track of which signs mean which, check out this article. The inequality crocodile is always hungry for the most it can get, om nom nom. How to Represent Inequalities We can represent inequalities in one of three different ways: A written expression A number line A graph Let's look at all three. Inequalities as written expressions use only mathematical symbols and no diagrams. They are exactly what we have been working with above (e.g., $y 37$). An inequality number line allows us to visualize the set of numbers that represents our inequality. We use a dark line to show all the numbers that match our inequality, and we mark where the inequality begins and/or ends in two different ways. To mark the beginning of an inequality that is "greater than" or "less than," we use an open circle. This shows that the starting number is NOT included. To mark the beginning of an inequality that is "greater than or equal to" or "less than or equal to," we use a closed circle. This shows that the starting number IS included. We can also combine these symbols if our inequality equation requires us to use two different symbols. For instance, if we have $-3 x ≠¤ 3$, our number line would look like: And finally, we can have inequalities in graphs for any and all types of graphs on the coordinate plane (more on the coordinate plane coming soon!). "Greater than" will be above the line of the graph, while "less than" will be below the line of the graph. Greater: This is true no matter which direction the line of the graph extends. Less: In terms of markings, inequality graphs follow the same rules as inequalities on number lines. Just as we use an open circle for "greater than" or "less than" inequalities, we use a dashed line for inequality graphs that are "greater than" or "less than." And just how we use a closed circle for "greater than or equal to" or "less than or equal to" inequalities, we use a solid line for our graphs that are greater or less than or equal to. And now to dive right in to ACT inequality problems! (Awkward flailing optional). Typical ACT Inequality Problems There are three different types of inequality questions you'll see on the ACT, in the order from most to least common: #1: Solve an inequality equation (find the solution set) #2: Identify or answer questions about an inequality graph or number line #3: Find alternate inequalities that fulfill given information Let's look at each type- what they mean and how you'll see them on the ACT. #1: Solving an Inequality Equation This is by far the most common type of inequality question you'll see on the ACT. You will be given one or two inequality equations and must solve for the solution set of your variable. Inequality problems work exactly the same way as a single variable equation and can be solved in the same way. Just think of the inequality sign as being the same as the equals sign. So you will perform the same actions (adding, subtracting, multiplying, and dividing) on each side. For instance: $9 + 12x 45$ $12x 36$ $x 3$ The only difference between equations and inequalities is that the inequality sign flips if you multiply or divide each side by a negative. For instance, $10 - 4x 50$ $-4x 40$ $x -10$ Because we had to divide each side by -4, we had to reverse the sign of the inequality. Alternatively, we can also use the strategy of plugging in answers (PIA) or plugging in numbers (PIN) to solve our inequality problems. Because all ACT math problems are multiple choice, we can simply test out which answers match our equation (and which do not) or we can choose our own values for x based on the information we know, depending on the problem. Let's look at an example of how this looks on the ACT, whether we solve the problem algebraically or by PIA. The inequality $3(x+2)4(x-3)$ is equivalent to which of the following inequalities? F. $x-6$G. $x5$H. $x9$J. $x14$K. $x18$ Solving Method 1: Algebra First, distribute out the variable on each side. $3(x + 2) 4(x - 3)$ $3x + 6 4x - 12$ Now, we must isolate our variable just as we would with a single variable equation. $6 x - 12$ $18 x$ Just as we saw back in our definitions, we know that we can also flip the inequality sign if we also switch the sides of our values. So $18 x$ is the same as saying $x 18$. Our final answer is K, $x 18$ Solving Method 2: Plugging in Answers Though it will often take a little longer, we can also solve our inequality problems by testing out the values in our answer choices. Let's, as usual when using PIA, start with answer choice C. Answer choice C says $x$ is less than 9, so let us see if this is true by saying that $x = 8$. If we plug in 8 for $x$ in the equation, we'll get: $3(x + 2) 4(x - 3)$ $3(8 + 2) 4(8 - 3)$ $3(10) 4(5)$ $30 20$ This is true, but that doesn't necessarily mean that it is the correct answer. Just because we know that $x$ can be equal to 8 or less doesn't mean it can't also be greater than 8. All we know for sure is that we can eliminate answer choices F and G, since we've problem that $x$ can be larger than each of them. So let us now go the opposite route and look at the highest value $x$ can be, given our answer choices. Answer choice J gives us $x 14$ and answer choice K says that $x 18$, so what would happen is we gave $x$ a value between the two? Let us say that $x = 16$ $3(x + 2) 4(x - 3)$ $3(16 + 2) 4(16 - 3)$ $3(18) 4(13)$ $54 52$ Because our inequality works for $x = 16$, we know that $x$ can be greater than $x 14$ and can, therefore, be greater than all the answer choices except for answer choice K (the answer choice that gives us our largest possible value for $x$). This is enough to tell us that our final answer is K. Our final answer is, again, K, $x 18$ #2: Inequality Graph and Number Line Questions For these types of questions, you will be asked to identify a graph or a number line from a given equation. Alternatively, you may be asked to infer information from a given inequality graph. Either way, you will always be given the graph on the coordinate plane. We know that the sum of $x$ and $y$ must be greater than 1, so let us imagine that one of those two variables is equal to 0. If we say that $x = 0$, then y alone has to be greater than 1 to make the sum of $x$ and $y$ still be greater than 1. We also know that we indicate that a value is "greater than" on a graph with a dashed line at the value in question and a filled in area above the value. The only graph with a dashed line at $y = 1$ and that has a shaded area above this value is graph J. This means graph J is more than likely our answer, but let's confirm it just to be safe. Because the sum of $x$ and $y$ must be greater than 1, the alternative possibility to $x = 0$ and $y 1$ is that $y$ equals zero, so $x$ must be greater than 1. To show this, we would need a dashed line at $(1, 0)$ and a shaded area above it, all of which graph J has. Now, to finish confirming that graph J is indeed our answer, we would simply do what we did to locate the lower limit of our graph in reverse so that we can find the upper limit. If $x + y 2$, then, when $x = 0$, $y$ must be less than 2, and when $y = 0$, $x$ must be less than 2. This would give us dashed lines at $(0, 2)$ and $(2, 0)$, both of which are on graph J. Our final answer is J. #3: Finding Alternate Inequality Expressions The rarest form of inequality questions on the ACT will ask you to use given inequalities and find alternate inequalities that must be true based off this given information. Let's look at one of these in action, to better see how this type of question works. If $x$ and $y$ are real numbers, such that $x1$ and $y-1$, then which of the following inequalities must be true? A. $x/y1$ B. $|x|^2|y|$ C. $x/3-5y/3-5$ D. $x^2+1y^2+1$ E. $x^{-2}y^{-2}$ There are two different ways we can solve this problem, by plugging in our own numbers or by working through it based on our logic and knowledge of algebra. We'll go through both methods here. Solving Method 1: Plugging in Numbers (PIN) Because we have a problem with multiple variables in both the problem and in the answer choices, we can make life a little easier and give our variables numerical values. Now, we do have to be careful when using this method, however, because there are infinite variables to choose from for both $x$ and $y$ and so more than one answer choice might work for any given variables we give to $x$ and $y$. If two or more answer choices work, we must simply pick new variables- eventually only the correct answer will be left, as it must work for ALL values of $x$ and $y$. When it comes to picking our values for $x$ and $y$, we can also make life easy by picking values that are easy to work with. We know that we must divide both $x$ and $y$ by 3 in answer choice C, so let us pick values that are divisible by 3, and we know we must square our values in several answer choices, so let us pick numbers that are fairly small. Now let's just say that $x = 6$ and $y = -9$ (Why those numbers? So long as they fulfill the given information- and they do- then why not!) And let us plug these values into our answer choices. Answer choice A gives us: $x/y 1$ If we plug in our values, we get: $6/{-9}$ $-{2/3}$ This is NOT greater than 1, so we can eliminate answer choice A. Answer choice B gives us: $|x|^2 |y|$ If we plug in our values, we get: $|6|^2 |-9|$ $36 9$ This is correct, so we will keep answer option B in the running for right now. Answer choice C gives us: $x/3 - 5 y/3 - 5$ If we plug in our values, we get: $6/3 - 6 {-9}/3 - 5$ $2 - 6 -3 - 5$ $-4 -8$ This is correct, so we will keep answer option C in the running for now as well. Because B and C are both correct, we will need to come back and test them both again with different values later. Answer choice D gives us: $x^2 + 1 y^2 + 1$ $6^2 + 1 -9^2 + 1$ $36 + 1 81 + 1$ $37 82$ This is NOT true, so we can eliminate answer choice D. Answer choice E gives us: $x^{-2} y^{-2}$ $6^{-2} -9^{-2}$ $1/{6^2} 1/{-9^2}$ $1/36 1/81$ Now this is indeed true, but what if we had chosen different values for x and y? Let's say that we said $x = 9$ and $y = -6$ instead (remember- so long as the numbers fit with the given information, we can use any values we like). $x^{-2} y^{-2}$ $9^{-2} -6^{-2}$ $1/{9^2} 1/{-6^2}$ $1/81 1/36$ Whoops! Answer choice E is no longer correct, which means we can eliminate it. We are looking for the answer choice that is always true, so it cannot possibly be answer E. Now we are left with answer choices B and C. Let's look at them each again. While we saw that our values for $x$ and $y$ meant that answer choice B was indeed true, let's see what would happen if we choose a much smaller value for $y$. Nothing is stopping us from choosing -6,000 for $y$- remember, all that we are told is that $y -1$. So let us use $y = -6,000$ instead. $|x|^2 |y|$ $|6|^2 |-6,000|$ $36 6,000$ This inequality is NOT true anymore, which means we can eliminate answer choice B. This means that answer choice C must be the right answer by default, but let's test it to make absolutely sure. Let us try what we did with answer option E and reverse the absolute values of our $x$ and $y$. So instead of $x = 6$ and $y = -9$, we will say that $x = 9$ and $y = -6$. $x/3 - 5 y/3 - 5$ $9/3 - 5 {-6}/3 - 5$ $3 - 5 -2 - 5$ $-2 -7$ No matter how many numbers we choose for $x$ and $y$, answer choice C will always be correct. Our final answer is C, $x/3 - 5 y/3 - 5$ Solving Method 2: Algebraic Logic As we can see, using PIN was successful, but required a good deal of time and trial and error. The alternative way to solve the problem is by thinking of how negatives and positives work and how exponents and absolute values alter these rules. We know that $x$ must be positive and $y$ must be negative to fulfill the requirements $x 1$ and $y -1$. Now let us look through our answer choices to see how these expressions are affected by the idea that $x$ must always be positive and $y$ must always be negative. Answer choice A gives us: $x/y 1$ We know that any fraction with a positive numerator and a negative denominator will be negative. And any negative number is less than 1. Answer choice A can never be correct. Answer choice B gives us: $|x|^2 |y|$ An absolute value means that the negative sign on $y$ has been negated, so this might be correct. But y can be any number less than -1, which means its absolute value could potentially be astronomically large, and $x$ can be any number greater than 1, which means its absolute value might be comparatively tiny. This means that answer choice B is not always correct, which is enough to eliminate it from the running. Answer choice C gives us: $x/3 - 5 y/3 - 5$ Now let's look at each side of the inequality. We know that any fraction with a positive number in both the numerator and in the denominator will give us a positive value. This means we will have some positive value minus 5 on the left side. We also know that any time we have a negative value in the numerator and a positive value in the denominator, we will have a negative fraction. This means we will have some negative value minus 5 on the right side. We also know that a negative plus a negative will give us an even greater negative (a smaller value). If we put this information together, we know that the left side may or may not be a negative value, depending on the value of $x$, but the right side will only get more and more negative. In other words, no matter what values we give to $x$ and $y$, the left side will always be greater than the right side, which means the expression is always true. Now this should be enough for us to select our right answer as C, but we should give a look to the other answer choices just in case. Answer choice D gives us: $x^2 + 1 y^2 + 1$ We know that if we square both a positive number and a negative number, we will get a positive result, so the negative value for $y$ is no longer in play. This inequality will therefore be true if the absolute value of $x$ is greater than the absolute value of $y$ (e.g., $x = 10$ and $y = -9$), but it won't be true if the absolute value of $y$ is greater than the absolute value of $x$ (e.g., $x = 9$, $y = -10$). This means that the inequality will sometimes be true, but not always, which is enough to eliminate it. Finally, answer choice E gives us: $x^{-2} y^{-2}$ We know that a number to a negative exponent is equal to 1 over that number to the positive exponent (e.g., $5^{-3} = 1/{5^3}$). This means that each value will be a fraction of 1 over the square of our $x$ and $y$ values. This will give us two positive fractions and $1/{x^2}$ will only be larger if the absolute value of $x$ is smaller than the absolute value of $y$. But, because our $x$ and $y$ values can be anything so long as $y$ is negative and $x$ is positive, this will only sometimes be true. We can therefore eliminate answer choice E. This leaves us with only answer choice C that is always true. Our final answer is C, $x/3 - 5 y/3 - 5$ "Win a war," "Rock the ACT"- we'd say the two are basically one and the same. ACT Math Strategies for Inequality Problems Though there are a few different types of inequality problems, there are a few strategies you can follow to help you solve them most effectively. #1: Write Your Information Down and Draw It Out Many problems on the ACT, inequalities included, appear easier or less complex than they actually are and can lead you to fall for bait answers. This illusion of ease may tempt you to try to solve inequality questions in your head, but this is NOT the way to go. Take the extra moment to work your equations out on the paper or even draw your own diagrams (or draw on top of the diagrams you're given). The extra few seconds it will take you to write out your problems are well worth the points you'll gain by taking the time to find the right answer. #2: Use PIN (or PIA) When Necessary If all you know about $x$ is that it must be more than 7, go ahead and pick a value for $\bi x$. This will help you more easily visualize and work through the rest of the problem, since it is generally always easier to work with numbers than it is to work with variables. As you use this strategy, the safest bet is to choose two values for your variable- one that is close to the definition value and one that is very far away. This will allow you to see whether the values you chose work in all instances. For instance, if all you know is $x 7$, it's a good idea to work through the problem once under the assumption that $x = 8$ and another time under the assumption that $x = 400$. If the problem must be true for all values $x 7$, then it should work for all numbers of $x$ greater than 7. #3: Keep Very Careful Track of Your Negatives One of the key differences between inequalities and single variable equations is in the fact that the inequality sign is reversed whenever you multiply or divide both sides by a negative. And you can bet the house that this is what the ACT will try to test you on again and again. Though the ACT is not engineered to trick you, the test-makers are still trying to challenge you and test whether or not you know how to apply key mathematical concepts. If you lose track of your negatives (an easy thing to do, especially if you're working in your head), you will fall for one of the bait answers. Keep a keen eye. #4: Double-Check Your Answer by Working Backwards (Optional) If you feel unsure about your answer for any reason (because so many of the answer choices look the same, because you're not sure if you handled the issue of negative numbers correctly, etc.), you can work backwards to see if your expression is indeed correct. For instance, let us look at the inequality we had earlier, when talking about the function of negatives on inequalities: $10 - 4x 50$ Again, we would go through this just as we would a single variable equation. $-4x 40$ $x -10$ But now maybe that answer doesn't feel right to you or you just want to double-check to be sure. Well, if we're told that $x$ must be greater than -10 to fulfill the inequality, let's make sure that this is true. Let us solve the expression with $x = -9$ and see if we are correct. $10 - 4x 50$ $10 - 4(-9) 50$ $10 + 36 50$ $46 50$ This is correct, so that's promising. But we found that $x$ needed to be greater than -10, so our expression should also be INCORRECT if $x$ were equal to -10 or if $x$ were less than -10. So let us see what happens if we have $x = -10$. $10 - 4x 50$ $10 - 4(-10) 50$ $10 + 40 50$ $50 50$ The inequality is no longer correct. This means that we know for certain that the solution set we found, $x -10$ is true. You will always be able to work backwards in this way to double-check your inequality questions. Though this can take a little extra time, it might be worth your peace of mind to do this whenever you feel unsure about your answers. Ready, set? It's test time! Test Your Knowledge Now let's put all that inequality knowledge to the test on some real ACT math problems. 1. The inequality $6(x+2)7(x-5)$ is equivalent to which of the following inequalities?A. $x-23$B. $x7$C. $x17$D. $x37$E. $x47$ 2. 3. If $r$ and $s$ can be any integers such that $s10$ and $2r+s=15$, which of the following is the solution set for $r$? A. $r≠¥3$B. $r≠¥0$C. $r≠¥2$D. $r≠¤0$E. $r≠¤2$ 4. Which of the following is the solution statement for the inequality shown below? $-51-3x10$ F. $-5x10$G. $-3x$H. $-3x2$J. $-2x3$K. $x-3$ or $x2$ 5. Answers: E, E, E, H, D Answer Explanations 1. This is a standard inequality equation, so let us go through our solve accordingly. First, let's begin by distributing out our equation. $6(x + 2) 7(x - 5)$ $6x + 12 7x - 35$ $12 x - 35$ $47 x$ Because we did not have to divide or multiply by a negative, we were able to keep the inequality sign intact. And because the expression $47 x$ and $x 47$ mean the same thing, we can see that this matches one of our answer choices. Our final answer is E, $x 47$ 2. We are given two graphs with equations attached and we must identify when one equation/graph is less than the other. We don't even have to know anything about what these equations means and we do not have to fuss with solving the equations- we can simply look at the diagram. The only place on the diagram where the graph of $y = (x - 1)^4$ is less than (aka lower than) the graph of $y = x - 1$ is between $x = 1$ and $x = 2$ on the coordinate plane. In other words, this inequality is true when $x 1$ and when $x 2$, or $1 x 2$. Our final answer is E, $1 x 2$. 3. We know that $s 10$ and it must be an integer, so let us make life easy and just say that $s = 11$. Now we can use this number to plug into the equation. $2r + s = 15$ $2r + 11 = 15$ $2r = 4$ $r = 2$ We know that $r$ can be equal to 2 and that it is the nearest integer to our definition. This means that our answer will either be C or E. So let us now find which direction our inequality sign must face. Let's now try one integer larger than 11 to see whether our solution set must be less or equal to 2 or greater than or equal to 2. If we say that $s = 12$, then our equation becomes: $2r + s = 15$ $2r + 12 = 15$ $2r = 3$ $r = 1.5$ We can see now that, as $s$ increases, $r$ will decrease. This means our solution set will be that $r$ is equal to or less than 2. Our final answer is E, $r≠¤ 2$ 4. Though this problem is made slightly more complex due to the fact that it is a double inequality expression, we still solve the inequality the same way we normally would. $-5 1 - 3x 10$ If we think of this expression as two different inequality equations, we would say: $-5 1 - 3x$ and $1 - 3x 10$ So let us solve each of them. $-5 1 - 3x$ $-6 -3x$ Because we now must divide by a negative, we must reverse the inequality sign. $2 x$ And now let's solve our second expression: $1 - 3x 10$ $-3x 9$ Again, we must reverse our inequality sign, since we need to divide each side by a negative. $x -3$ Now, if we put the two results together, our expression will be: $-3 x 2$ Our final answer is H, $-3 x 2$ 5. Because we have a number line with two closed circles, we know that must use less than or equal to and greater than or equal to signs. We can see that the right side of the graph gives us a set of numbers equal to or greater than 3, which means: $x ≠¥ 3$ The left side of the graph gives us a set of numbers less than or equal to -1, which means: $x ≠¤ -1$ Our final answer is, therefore, D, $-1 ≠¥ x$ and $x ≠¤ 3$. And now, your reward for solving your inequality problems is oodles of Cuteness. The Take-Aways Inequalities are so similar to single variable equations that it can be easy to treat the two as the same. The test-makers know this, so it pays to be careful when it comes to your inequality questions. Remember the key differences (multiplying or dividing by a negative reverses the sign, and you can flip your inequality signs so long as you flip both sides of the expression) and keep careful track of the details to avoid all the common pitfalls and bait answers. After you've mastered the art of answering your inequality questions, that's another 5% of the test that you've dominated. You're well on your way to that score goal of yours now! What's Next? Want to brush up on any of your other math topics? Check out our individual math guides to get the walk-through on each and every topic on the ACT math test. Been procrastinating on your ACT studying? Learn how to get over your desire to procrastinate and make a well-balanced study plan. Running out of time on the ACT math section? We'll teach you how to beat the clock and maximize your ACT math score. Looking to get a perfect score? Check out our guide to getting a perfect 36 on ACT math, written by a perfect-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. 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