A-6 Answers to Selected Exercises 96. –2 –6 0 4 3 97. In the interval 1-∞, -62, choose x = -10, for example. It satisfies the original inequality. In the interval 1-6, -22, choose x = -4, for example. It does not satisfy the inequality. In the interval A -2, 4 3B , choose x = 0, for example. It satisfies the original inequality. In the interval A4 3 , ∞ B , choose x = 4, for example. It does not satisfy the original inequality. 98. (a) –2 –6 0 4 3 (b) 1-∞, -64 ´C -2, 4 3D 99. C -2, 3 2D ´33, ∞2 101. 1-∞, -24 ´30, 24 103. 1-∞, -12 ´1-1, 32 105. 3-4, -34 ´33, ∞2 107. 1-∞, ∞2 1.8 Exercises 1. F 3. D 5. G 7. C 9. E - 1 3 , 1F 11. E 2 3 , 8 3F 13. 5-6, 146 15. E5 2 , 7 2F 17. E - 4 3 , 2 9F 19. E - 7 3 , - 1 7F 21. 516 23. 1-∞, ∞2 25. A positive solution will return a negative quantity for -5x, and the absolute value of an expression cannot be negative. 27. 1-4, -12 29. 1-∞, -44 ´3-1, ∞2 31. A - 3 2 , 5 2B 33. 1-∞, 02 ´16, ∞2 35. A -∞, - 2 3B ´14, ∞2 37. C - 2 3 , 4D 39. C -1, - 1 2D 41. 1-101, -992 43. E -1, - 1 2F 45. 52, 46 47. A - 4 3 , 2 3B 49. A - 3 2 , 13 10B 51. A -∞, 3 2D ´C 7 2 , ∞B 53. ∅ 55. 1-∞, ∞2 57. ∅ 59. E - 5 8F 61. ∅ 63. E - 1 2F 65. A -∞, - 2 3B ´A - 2 3 , ∞B In Exercises 67–73, the expression in absolute value bars may be replaced by its additive inverse. For example, in Exercise 67, p −q may be written q −p. 67. p - q = 2 69. m- 7 … 2 71. p - 9 60.0001 73. r - 29 Ú 1 75. 10.9996, 1.00042 77. 36.7, 9.74 79. F - 730 … 50 81. 25.33 … RL … 28.17; 36.58 … RE … 40.92 83. -6 or 6 84. x 2 - x = 6; 5-2, 36 85. x2 - x = -6; U1 2 { 123 2 i V 86. U -2, 3, 1 2 { 123 2 i V 87. U - 7 3 , 2, - 1 6 { 1167 6 i V 89. U -1 3 , 5, 7 3 { 234 3 V 91. 5-4, -3, -2, -16 93. 5-3, 2, 46 95. E - 1 4 , 6F 97. 5-1, 16 99. ∅ 101. A -∞, - 1 3B ´A - 1 3 , ∞B Chapter 1 Review Exercises 1. 566 3. E - 11 3 F 5. ƒ = AB1 p + 12 24 7. A, B 9. 13 in. on each side 11. 3 3 7 L 13. 560 km per hr 15. (a) A = 36.525x (b) 2629.8 mg 17. (a) $4.31; The model gives a figure that is $0.51 more than the actual figure of $3.80. (b) 47.6 yr after 1956, which is mid-2003. This is close to the minimum wage changing to $5.85 in 2007. 19. 13 - 3i 21. -14 + 13i 23. 19 + 17i 25. 146 27. -30 - 40i 29. 1 - 2i 31. -i 33. i 35. i 37. E -7{15F 39. E -3, 5 2F 41. E - 3 2 , 7F 43. E2{16F 45. U 15 {3 2 V 47. D 49. 76; two distinct irrational solutions 51. -124; two distinct nonreal complex solutions 53. 0; one rational solution (a double solution) 55. 6.25 sec and 7.5 sec 57. 1 2 ft 59. $1029.1 billion 61. E{i, { 1 2F 63. E - 7 24F 65. ∅ 67. 5-239, 2476 69. 51, 46 71. 5-2, -16 73. 536 75. ∅ 77. 5-16 79. E - 7 4F 81. E -15, 5 2F 83. A - 7 13 , ∞B 85. 1-∞, 14 87. 34, 54 89. 3-4, 14 91. A - 2 3 , 5 2B 93. 1-∞, -44 ´30, 44 95. 1-∞, -22 ´15, ∞2 97. 1-2, 02 99. 1-3, 12 ´37, ∞2 101. (a) 79.8 ppb (b) 87.7 ppb 103. (a) 20 sec (b) between 2 sec and 18 sec 105. The value 3 makes the denominator 0. Therefore, it must be excluded from the solution set. 107. 5-11, 36 109. E11 27 , 25 27F 111. E - 2 7 , 4 3F 113. 3-6, -34 115. A -∞, - 1 7B ´11, ∞2 117. A - 17 3 , 1B 119. 1-∞, ∞2 121. 50, -46 123. k - 6 = 12 1or 6 - k = 122 125. t - 5 Ú 0.01 1or 5 - t Ú 0.012 Chapter 1Test [1.1] 1. 506 2. 5-126 [1.4] 3. E - 1 2 , 7 3F 4. U -1 {2 12 3 V 5. U - 1 3 { 15 3 i V [1.6] 6. ∅ 7. E - 3 4F 8. 546 9. 5-3, 16 10. 5-26 11. 5{1, {46 12. 5-30, 56 [1.8] 13. E - 5 2 , 1F 14. E -6, 4 3F [1.1] 15. W= S - 2LH 2H + 2L [1.3] 16. (a) 5 - 8i (b) -29 - 3i (c) 55 + 48i (d) 6 + i 17. (a) -1 (b) i (c) i [1.2] 18. (a) A = 806,400x (b) 24,192,000 gal (c) P = 40.32x; 40 pools (d) 25 days 19. length: 200 m; width: 110 m 20. cashews: 23 1 3 lb; walnuts: 11 2 3 lb 21. 15 mph [1.2] 22. (a) 1.5% (b) 2010 [1.5] 23. (a) 1 sec and 5 sec (b) 6 sec [1.7] 24. 1-3, ∞2 25. 3-10, 24 26. 1-∞, -14 ´C 3 2 , ∞B 27. 1-∞, 32 ´14, ∞2 [1.8] 28. 1-2, 72 29. 1-∞, -64 ´35, ∞2 30. E - 7 3F
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