Answers for Lesson 4-1, pp

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1 Answers for Lesson -, pp yes. no. yes. yes 5. no 6. yes 7. no 8. yes Exercises 9. a. no b. no c. yes 0. a. yes b. no c. yes. a. no b. no c. no. a. yes b. no c. no. a. no b. yes c. no. a. no b. no c. yes 5. C 6. B 7. D 8. A Choice of variable may vary. 7. x x # 7 9. x $ 0. x, -6. x $.5. x, Let s = number of students. s # 8. Let a = age. a $ 6 5. Let w = acceptable number of watts. w # Let s = number of students. s $ Algebra Chapter 7

2 Answers for Lesson -, pp Let a = number of appearances. a n is less than b is greater than is greater than or equal to x, or x is less than or equal to 7.. z is greater than or equal to q is less than, or is greater than q.. - is greater than or equal to m, or m is less than or equal to is greater than or equal to w, or w is less than or equal to g minus is less than a is less than or equal to plus r is greater than is less than or equal to h, or h is greater than or equal to is greater than k, or k is less than Use an open dot for, or.. Use a closed dot for # or $. 5. Answers may vary. Sample: Every class has at least 8 students. 5. D 5. x. 5. b # r $ a, Algebra Chapter 7

3 Answers for Lesson -, pp At least is translated as $. At most is translated as #. 6. x $ Option A, Option B 66. Answers may vary. Sample: For x =-, (-) + =- + = Put an open dot at and color the rest of the number line. 68. greater than x means x + ;. x means is greater than x. 69. C; the inequality is true for x = but not true for x = 5, so C is correct. 70. Answers may vary. Sample: a =-, b = 7. a is negative, and a and b are opposites Algebra Chapter 7

4 Answers for Lesson -, pp Exercises x. 5. t, 6. b, - 7. d $ 0 8. s $ - 9. r # 9 0. n. 0. w #. d.. y # -. q, 5. x $.5 6. r,.5 7. m, b, 9. n Algebra Chapter 7

5 Answers for Lesson -, pp w # 5;. m. -8; 5. b. -7; 6. a # -6; 7. r $ -6; 8. k # ; 9. x, -; 0. p. -6;. z $ -;. y, 5.5;. m. - ;. a # -0.; 5. p. -7; 6. h # - ; d. -.5; 8. t, - ; Algebra Chapter 75

6 Answers for Lesson -, pp s + 67 # 000, $6 0. s # 5, $.50. r $ 50, reflectors. Add to each side.. Subtract 9 from each side.. Add to each side. 5. w $ 6. c # 7. y,. 8. n, 5 9. z, y, t. 5. v $ 6 5. k $ b, m # k # 57. h $ 58. x # w, 60. at least $ a. yes b. no 5 c. Answers may vary. Sample: The = sign indicates that each side is equal, so the two sides may be interchanged. The, sign does not indicate equality. One side cannot be both greater than and less than the other side. 6. a. Let n = points scored on floor exercises n $.0; n $ 9. b. Your sister must score 9. points or more to qualify for regional gymnastics competition. c. Answers may vary. Sample: 9., 9., nearly 5. MB 6. 0 or more points Algebra Chapter 76

7 Answers for Lesson -, pp a-b. Check students work. 66. a. No; the solution is z $.8, so z $ is not correct. b. Answers may vary. Sample: Substituting values does not work because there is always the possibility that the solution lies between values that make the inequality true and a value that does not. 67. x $ 68. n, t # k a # 7. a, a. a. c - b b. b. a - c c. c. b - a d. The length of the third side must be greater than the difference of the lengths of the other two sides. 7. not true; sample counter example: for a = 5 and b =-6, 5 -(-6) 5 5 +(-6) 75. true 76. true 77. not true; sample counter example: for a = 0, b =, and c =-, 0, and (-) 78. Answers may vary. Sample: For x =, y =, z =, and w =,. and., but Algebra Chapter 77

8 Answers for Lesson -, pp t $ -;. s, 6;. w # -;. p, -8; 5. y. -; 6. v # -.5; 7. x, 6; 8. k $ -; 9. x, 0; 0. y $ 0;. x, 7;. d $ -;. c. - ;. b $ - ; 5. u, - ; 6. n. ; 7. t, -; Exercises Algebra Chapter 78

9 Answers for Lesson -, pp m $ ; 9. w # -5; 0. c. ;. z # -9;. b, -6;. d, - ;. x $ 5 ; 5. q. - ; 6. h, 5; 7. d. ; 8. m # -.5; c $ 00, 67 cars h $ 00, 7 hours Answers may vary. Samples are given.. -, -, -, -5. -, -0, -8, 0. -, -, -5, -6.,0,-, , -7, -8, , -, -, ,,, , -, -, - Algebra Chapter 79

10 Answers for Lesson -, pp Multiply each side by - and reverse the inequality symbol. 0. Multiply each side by 5.. Divide each side by 5.. Multiply each side by.. Divide each side by.. Multiply each side by - and reverse the inequality symbol x and y are equal Estimates may vary. 5. r j p # 55. s $ concrete blocks 57. For both the equation and the inequality, you multiply each side by -. For the inequality, you must reverse the inequality symbol. 58. Answers may vary. Sample: x. 6, x., -x,, -, d # u s, 6. k $ y, 9 6. t # h # x. 67. x, b, p m # -7 x g, - 7. n $ 7. m,.5 Algebra Chapter 80

11 Answers for Lesson -, pp z $ Yes; in each case, y is greater than , r; r a. She should have divided each side by -5. b. 50 satisfies the original inequality -5q # 5. c. Answers may vary. Sample: a a a? 0 8. a, 0 8. pd. 5, 5-in. box or 6-in. box x $ 8(5), 80 tiles Algebra Chapter 8

12 Answers for Lesson -, pp. Exercises. d #. m. -. x. -. n # 5. q $ 6. h $ - 7. a # 8. b c, 0. 8t $ 0 and t $ 5.5, so the average rate of speed must be at least 5.5 mi/h.. 7 $ s + 8 and s # 9.5, so the two equal sides must be no longer than 9.5 cm.. -6x + 9. j $. b, 5. h x $ 7. y w # 9. c, r #. n # 9. w,. t # -. d # 6 5. n $ 6. k $ - 7. s, 0 8. p. 9. x. 0. m. -. v $ -. q # -. r $. x, 5. m v $ 5 7. Subtract 8 from each side. 8. Subtract 7 from each side. 9. Subtract y from each side and add 5 to each side. 0. Add to each side, then multiply each side by -5, and reverse the inequality sign. Algebra Chapter 8

13 Answers for Lesson -, pp.. Answers may vary. Sample: To solve.5(p - ). (p + ), first use the Distributive Property to simplify each side. The result is.5p - 0. p + 6. Then use the Subtraction Property of Inequality. Subtract 6 from each side and.5p from each side. The result is p. Then use the Division Property of Inequality. Divide each side by 0.5. The result is -. p. So the solution is -. p or p, -.. C. For x = the number of guests, (0.75)00 +.5x $ 50; x $ 80; at least 80 guests must attend.. a. maximum b. no more than 5 5. B 6. E 7. F 8. A 9. D 50. C 5. Answers may vary. Samples: - x , x, -5; - x - 5 # 0, x $ r, 5 5. m $ 5. s #. 55. n # 56. s, k #. 58. n. 59. r # 60. x. 6. a $ 6. m $ 6. k # 6. n $ 65. x # a, c $ a. -t # -9, t $ b. 9 # t, t $ c. The results are the same. 6 Algebra Chapter 8

14 Answers for Lesson -, pp. 69. a. i. always true ii. always true iii. never true b. If the coefficients of the only variable on each side of an inequality are the same, then the inequality will either be always true or never true. 70. For x = amount of sales, x $ 60, so to reach her goal, she must have at least $7000 in sales. 7. a. x, n; the greater values in the table make the inequality false. b. Sample:. c. x, ; this is close to the estimate. 7. Add x to each side rather than subtract x, so x #. 7. Distribute to as well as n, so n a. x. b. x, 75. x is an integer between - and 7, inclusive in.. in h 79. a. 7 boxes b. 5 trips c b a c b a 5 Algebra Chapter 8

15 Answers for Lesson -5, pp. 9. -, x and x, 6 or -, x, 6;. # n and n # 9, or # n # 9;., c,.5;. 0 # w # 7; 5. -5, j, 5; 6. # w # 5; 7., n # 6; 8. -, p # -; 9., x, ; , w #.5;. 5, x, 8;. -, m # ;. # s, ;. 5 # a # 7; 5., x, 7; 6. - # x # ; 7. n # - or n $ 5, Exercises Algebra Chapter 85

16 Answers for Lesson -5, pp x, or x. 7; 9. h, or h. ; 0. b, 00 or b. 00;. b, - or b. ;. k, -5 or k. -;. c, or c $ ;. a # or a. 5; 5. c # or c $ ; 6. y # - or y $ 5; 7. d # - or d $ 0; 8. z, - or z. ; 9. -, x, 0. x, - or x $. x # 0 or x.. - # x # q # - or q.. h, -7 or h. 5. # t # 6. r, 6 or r # t, 8. x, -6 or x D 0. all real numbers except 5. The word and means both statements must be true. The word or means that at least one of the statements must be true. Algebra Chapter 86

17 Answers for Lesson -5, pp. 9..5, x, , x, 0. 7, x, 9 5., x, # C # # D # 0 8. Charlotte: 9 # C # 90 Detroit: 5 # D # 8 9. Answers may vary. Sample: Elevation near a coastline varies between m below and 8 m above sea level. 50. tepid warm hot , x, 0 or 0, x, 5. n = 0 or n $ 5. a. 0 # R # 57 b. 0 years old 5. 6, 8, ,, Algebra Chapter 87

18 Answers for Lesson -6, pp. 7 9 Exercises. -,. -,. -,. -6, , 6. -7, , , no solution. -,. -,.,. -8, 5. -, 6. -5, 7. -5, 9 8. no solution 9. -7, 0. -,. -0.6, 0.6. a. less than b. greater than. k, -.5 or k..5;. -, w, ; 5. -8, x, ; 6. n # - or n $ -5; 7. # y # ; 8. # p # 7; 9. -, c, 7; 0. y # - or y $ 5;. t, - or t. ;. x, - or x..5; Algebra Chapter 88

19 Answers for Lesson -6, pp t # -. or t $ ;. -, r, 8; 5. between.8 mm and.0 mm, inclusive 6. between 9 in. and 50 in., inclusive 7. -9, , 9. -, ,.8. -5,. 0, 8. d # or d $. n, -0 or n c, -6 or c , , x, , , , 5. -8, m, 5. n«, 5. n« n - 6«. 55. n + «$ 56. w - 6«# 0.05, 5.95 # w # %, 5% a. w - 5«# 5 b. between 9 g and 59 g, inclusive 59. g - 6.7«# The absolute value of a number cannot be less than zero. 6. Sample: 5x - «=;, x - «= 6. x - «= 7 5 Algebra Chapter 89

20 Answers for Lesson -6, pp x - «=6 65. x - «= 66. x - «= 67. x - 5 «= 68. x + 9«=6 69. x - 6«= 70. a. between oz and 7.05 oz, inclusive b. No; the excess weight of some coins may be balanced by the lower weight of other coins. 7. a. 8F,98F b. t - 5«= 7. 7., # 76. $ 77. = 78. = 79. x + «. 80. x - «# Algebra Chapter 90