LearningExpress Skill Builders • CHAPTER 4 99 x 1 . To divide x 4 by x 1 , you just subtract 4 Ϫ 1, to get x 3 . The equation is now ( ᎏ x y 3 ᎏ )( ᎏ 3 7 y 3 ᎏ ). We divide y 3 by y, to get y 2 in the numerator. (x 3 )( ᎏ 3 7 y 2 ᎏ ) = ᎏ 3x 7 3 y 2 ᎏ . 6. a. First, subtract 4 from both sides of the equa- tion 2x ϩ 4 ϽϪ12 to yield 2x ϽϪ16. Next, divide everything by 2 to get x ϽϪ8. 7. c. Substitute Ϫ5 in for b in the given equation. Thus, ( ᎏ 1 6 ᎏ )(b 2 ϩ b) = ( ᎏ 1 6 ᎏ )(Ϫ5 2 ϩ 5) ϭ ᎏ 1 6 ᎏ (25 Ϫ 5) ϭ ᎏ 1 6 ᎏ (20) ϭ ᎏ 2 6 0 ᎏ ϭ ᎏ 1 3 0 ᎏ . 8. d. Put Ϫ2 in for x in the equation 3x 2 Ϫ 2x ϩ 5. Thus, the equation becomes 3(Ϫ2) 2 Ϫ 2(Ϫ2) ϩ 5 ϭ 3(4) Ϫ (Ϫ4) ϩ 5 ϭ 12 ϩ 4 ϩ 5 ϭ 21. 9. d. If b is greater than 5, then you can write b Ͼ 5. In order to compare this to b ϩ 3, just add 3 to both sides of the inequality: b ϩ 3 Ͼ 5 ϩ 3, or b + 3 > 8. Thus, b ϩ 3 must be greater than 8. 10. a. (x ϩ 2) 2 ϭ 4x can be rewritten as (x Ϫ 2) (x Ϫ 2) ϭ 0. So you know that x Ϫ 2 ϭ0, or x ϭ2. 11. b. 5x Ϫ 6 ϭ 3x ϩ 16 can be simplified by first sub- tracting 3x from both sides to yield 2x Ϫ 6 ϭ 16. Now, you add both 6 to both sides to get 2x ϭ 22. Dividing both sides by 2, you get x ϭ 11. 12. d. Replace every q with a 6 in the equation 5q Ϫ q 2 to yield 5(6) Ϫ (6) 2 ϭ 30 Ϫ 36 ϭϪ6. 13. d. x 2 ϩ 2x Ϫ 15 ϭ 0 can be factored into two sets of parentheses: (x ± ?)(x ± ?). Because the coeffi- cient on the x 2 is 1, we know the missing num- bers add to 2 (because the coefficient of x is 2) and multiply to Ϫ15 (the lone number is Ϫ15). Thus, the numbers are Ϫ3 and ϩ5. The equation is equivalent to (x Ϫ 3)(x ϩ 5) ϭ 0. This means x Ϫ 3 ϭ 0 and x ϩ 5 ϭ 0, or x ϭ 3 and x ϭϪ5, respectively. 14. c. Ϫ5x Ϫ 5 ϭ 30 can be simplified by first adding 5 to both sides: Ϫ5x ϭ 35. Next, divide by Ϫ5 to yield x ϭϪ7. 15. a. Divide both sides of Ϫ3x Ͻ 9 by Ϫ3, but be sure to flip the sign! Thus, you get x ϾϪ3. 16. a. (8x 3 y)(2x 5 y 9 ) can first be reduced to 16x 3 yx 5 y 9 . If you have the same base, when multiplying exponents, remember to just add the powers. For the x terms, you add 3 ϩ 5 to get x 8 . Since y is the same as y 1 , when you add the powers of the y terms you get 1 ϩ 9, or y 10 . Thus, the final answer is 16x 8 y 10 . 17. c. The given equation is 9(P ϩ 1) ϾϪ2(ϪP ϩ 2.5). First, we distribute the 9 to get 9P ϩ 9 ϾϪ2 (ϪP ϩ 2.5). Next, we distribute the Ϫ2 and the inequality becomes 9 P ϩ 9 Ͼ (Ϫ2 )(ϪP) ϩ (Ϫ2)(2.5), or 9P ϩ 9 Ͼ 2P ϩ (Ϫ5), or 9P ϩ 9 Ͼ 2P Ϫ5. Now we subtract 2P from both sides to get 7P ϩ 9 ϾϪ5. Then, we subtract 9 from both sides to get 7P ϾϪ14. Finally, divide by 7 to get P Ͼ Ϫ2. 18. b. He starts with $20 but we have to subtract the cost of the three psychology books and the cost of the vocabulary book in order to figure out his change. Three psychology books at $3.25 each would be represented as 3 ϫ 3.25 or 3(3.25). We have 20 Ϫ 3(3.25) Ϫ 5 ϭ C. 19. b. The expression 3x 2 Ϫ x Ϫ 2 ϭ 0 can be factored into two sets of parentheses: (3x ± ?)(x ±?). Because the coefficient on the x 2 is not 1, focus your attention on the lone number, Ϫ2, which indicates that the numbers you will stick in the parentheses have a product of Ϫ2. The numbers will be a combination of Ϫ1 and 2 or 2 and Ϫ1. Because one set of parentheses has a 3x,placement –ESSENTIAL PRACTICE WITH MATH– CHAPTER 4 • LearningExpress Skill Builders 100 will matter and you have to just test out all com- binations until one works. The working combi- nation is (3x ϩ 2)(x Ϫ 1) ϭ 0. Next, you solve for x. (3xϩ 2) (x Ϫ 1) ϭ 0 3x ϩ 2 ϭ0 x Ϫ 1ϭ0 3x ϭϪ2 x ϭ 1 x ϭϪ ᎏ 2 3 ᎏ Only Ϫ ᎏ 2 3 ᎏ is listed as an answer choice. 20. d. B 2 ϩ 8B ϩ 12 ϭ 0 can be factored into two sets of parentheses: (B ± ?)(B ± ?). Because the coeffi- cient on the B 2 is 1, we know the missing num- bers add to 8 (because the coefficient of B is 8) and multiply to 12 (the lone number is 12). Thus, the numbers are 6 and 2, and the equation is (B ϩ 6)(B ϩ 2) ϭ 0. Solving for B,we get: (B ϩ 6 ) (B ϩ 2) ϭ 0 Bϩ6 ϭ0 B ϩ 2 ϭ0 B ϭϪ6 B ϭϪ2 21. a. Take the given equation, 2x 3 ϩ 8 ϭ 62, and sub- tract 8 from both sides to yield 2x 3 ϭ 54. Next, divide both sides by 2 to get x 3 ϭ 27. (x)(x)(x) ϭ 27, or x ϭ3. 22. d. Notice that all the answer choices are expressed as fractions. That’s your clue that you need to find a common denominator for these terms. The denominators are 3, 10, and 5, so 30 would be a great common denominator.To turn ᎏ 3 x ᎏ into some- thing over 30, you are multiplying top and bot- tom by 10. This first term becomes ᎏ 1 3 0 0 x ᎏ .Now look at the second term, ᎏ 1 3 0 x ᎏ . To turn this term into something over 30, you’ll multiply top and bot- tom by 3, yielding ᎏ 3 9 0 x ᎏ . Next, to turn ᎏ 2 5 x ᎏ into some- thing over 30, multiply top and bottom by 6, and you get ᎏ 1 3 2 0 x ᎏ . The original expression ( ᎏ 3 x ᎏ ) ϩ ( ᎏ 1 3 0 x ᎏ ) Ϫ ( ᎏ 2 5 x ᎏ ) is now ( ᎏ 1 3 0 0 x ᎏ ) ϩ ( ᎏ 3 9 0 x ᎏ ) Ϫ ( ᎏ 1 3 2 0 x ᎏ ) ϭ ᎏ 3 7 0 x ᎏ . 23. c. Starting with 2x Ϫ y ϭ 4 and x ϩ y ϭ 8, rewrite them as 2x Ϫ 4 ϭ y and 8 Ϫ y ϭ x. Substitute the first expression into the second: 8 Ϫ 2(2x Ϫ 4) ϭ x and solve for x; this yields 12 ϭ 3x or 4 ϭ x. 24. a. Substituting x ϭ 3 and y ϭϪ2 into the equa- tion 5x 2 ϩ 2xy 3 we get: 5(3) 2 ϩ 2(3)(Ϫ2) 3 ϭ (5)(9) ϩ (2)(3)(Ϫ8) ϭ 45 ϩ (6)(Ϫ8) ϭ 45 ϩ (Ϫ48) ϭ Ϫ3. 25. c. When you substitute a ϭ 2, b ϭϪ1, and c ϭ ᎏ 1 2 ᎏ , into the expression ᎏ 2a Ϫ c b ϩ 5 ᎏ you get: which simplifies to: which equals: 10 divided by ᎏ 1 2 ᎏ is the same thing as 10 times 2, which equals 20. 10 ᎏ ᎏ 1 2 ᎏ 4 ϩ1 ϩ 5 ᎏᎏ ᎏ 1 2 ᎏ 2(2) Ϫ (Ϫ1) ϩ 5 ᎏᎏ ᎏ 1 2 ᎏ –BASIC SKILLS FOR COLLEGE– LearningExpress Skill Builders • CHAPTER 5 101 C • H • A • P • T • E • R SUMMARY This chapter gives you the chance to apply what you have learned. Included are practice tests in grammar, writing, and reading comprehension. As you complete the sections, you should be able to find your strengths and weaknesses. PRACTICE TESTS IN GRAMMAR, WRITING, AND READING COMPREHENSION 5 5 CHAPTER 5 • LearningExpress Skill Builders 102 PRACTICE GRAMMAR TEST AGREEMENT There is an agreement error in each of the following sentences. Mark an SV to the left of the sentence if there is a subject/verb error. Mark a PA to the left if there is a pronoun/antecedent error. Then try rewriting the sentence correctly. ______ 1. It is unacceptable to clone a child because they would be treated as second class and not as a tradi- tional being. _____________________________________________________________________________ _____________________________________________________________________________ ______ 2. By euthanizing terminally ill patients, doctors will be relieved of the time they spend treating these patients, and he or she will have more time to spend with patients they can really cure. _____________________________________________________________________________ _____________________________________________________________________________ ______ 3. Many incidents of condensed air pollution has killed or hospitalized hundreds of people at a time. _____________________________________________________________________________ _____________________________________________________________________________ ______ 4. The principle of the issue is still over legalizing the right to help someone end their life. _____________________________________________________________________________ _____________________________________________________________________________ ______ 5. The author’s focal point throughout his arguments are that human cloning would diminish family relationships. _____________________________________________________________________________ _____________________________________________________________________________ ______ 6. In conclusion, air and garbage pollution is a real problem for Americans. _____________________________________________________________________________ _____________________________________________________________________________ –BASIC SKILLS FOR COLLEGE– LearningExpress Skill Builders • CHAPTER 5 103 ______ 7. The list of candidates for graduation include my name and my brother’s. _____________________________________________________________________________ _____________________________________________________________________________ ______ 8. My books and my calculator remains in the test room. _____________________________________________________________________________ _____________________________________________________________________________ ______ 9. Her problem are migraine headaches. _____________________________________________________________________________ _____________________________________________________________________________ ______ 10. Each of the episodes on ER and NYPD Blue is exciting. _____________________________________________________________________________ _____________________________________________________________________________ SENTENCE STRUCTURE There is a sentence fragment, fused sentence, or comma splice error in each sentence below. First, mark an SF for sentence fragment, a FS for fused sentence, or a CS for comma splice to the left of the sentence. Then rewrite the sentence correctly. ______ 1. The two-car family is common these days everyone wants an SUV and a sedan. _____________________________________________________________________________ _____________________________________________________________________________ ______ 2. Roses are not difficult to grow, they just need to be fed and pruned regularly. _____________________________________________________________________________ _____________________________________________________________________________ ______ 3. California often endures brush fires that are hard to put out, some have been burning for years. _____________________________________________________________________________ _____________________________________________________________________________ –PRACTICE TESTS IN GRAMMAR, WRITING, AND READING COMPREHENSION– CHAPTER 5 • LearningExpress Skill Builders 104 ______ 4. Some villagers had never seen an automobile. Only knowing bicycles as a means of transportation. _____________________________________________________________________________ _____________________________________________________________________________ ______ 5. Environmentalists fear that once the Alaska oil fields are opened for exploration, wilderness will be destroyed. With no guarantees that our energy crisis will have been helped in the process. _____________________________________________________________________________ _____________________________________________________________________________ ______ 6. Recent census figures indicate that there has been a dramatic increase in the number of men who are single parenting their children, the mothers gave up custody during the divorce proceedings. _____________________________________________________________________________ _____________________________________________________________________________ ______ 7. Human cloning is just years if not months away do we fully understand the social consequences of our research? _____________________________________________________________________________ _____________________________________________________________________________ ______ 8. Testing cosmetics by using helpless animals is cruel, there should be laws to protect against such abuse. _____________________________________________________________________________ _____________________________________________________________________________ ______ 9. Weather maps, graphs, charts, tables. All are confusing to read. _____________________________________________________________________________ _____________________________________________________________________________ ______ 10. Hurricanes are dangerous storms costing thousands of dollars to homeowners in repair costs each year, Congress should pass more laws to help citizens in crises such as these. _____________________________________________________________________________ _____________________________________________________________________________ –BASIC SKILLS FOR COLLEGE– . ( ᎏ 1 6 ᎏ )(b 2 ϩ b) = ( ᎏ 1 6 ᎏ )(Ϫ5 2 ϩ 5) ϭ ᎏ 1 6 ᎏ (25 Ϫ 5) ϭ ᎏ 1 6 ᎏ (20 ) ϭ ᎏ 2 6 0 ᎏ ϭ ᎏ 1 3 0 ᎏ . 8. d. Put 2 in for x in the equation 3x 2 Ϫ 2x ϩ 5. Thus, the equation becomes 3( 2) 2 Ϫ 2( 2) ϩ 5. this yields 12 ϭ 3x or 4 ϭ x. 24 . a. Substituting x ϭ 3 and y ϭ 2 into the equa- tion 5x 2 ϩ 2xy 3 we get: 5(3) 2 ϩ 2( 3)( 2) 3 ϭ (5)(9) ϩ (2) (3)(Ϫ8) ϭ 45 ϩ (6)(Ϫ8) ϭ 45 ϩ (Ϫ48) ϭ Ϫ3. 25 . c. When. 9(P ϩ 1) Ͼ 2( ϪP ϩ 2. 5). First, we distribute the 9 to get 9P ϩ 9 Ͼ 2 (ϪP ϩ 2. 5). Next, we distribute the 2 and the inequality becomes 9 P ϩ 9 Ͼ ( 2 )(ϪP) ϩ ( 2) (2. 5), or 9P ϩ 9 Ͼ 2P ϩ (Ϫ5),