186 CHAPTER 1 Equations and Inequalities Solve each equation or inequality. See Examples 3 and 4. 43. 4x + 3 - 2 = -1 44. 8 - 3x - 3 = -2 45. 6 - 2x + 1 = 3 46. 4 - 4x + 2 = 4 47. 3x + 1 - 1 62 48. 5x + 2 - 2 63 52. 12 - 6x + 3 Ú 9 53. 3x - 7 + 1 6 -2 54. -5x + 7 - 4 6 -6 Write each statement using an absolute value equation or inequality. See Example 5. 69. m is no more than 2 units from 7. 70. z is no less than 5 units from 4. 71. p is within 0.0001 unit of 9. 72. k is within 0.0002 unit of 10. 73. r is no less than 1 unit from 29. 74. q is no more than 8 units from 22. 76. Tolerance Suppose that y = 10x + 2 and we want y to be within 0.003 unit of 5. For what values of x will this be true? 77. Weights of Babies Dr. Tydings has found that, over the years, 95% of the babies he has delivered weighed x pounds, where x - 8.2 … 1.5. What range of weights corresponds to this inequality? 78. Temperatures on Mars The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality C + 84 … 56. What range of temperatures corresponds to this inequality? 79. Conversion of Methanol to Gasoline The industrial process that is used to convert methanol to gasoline is carried out at a temperature range of 680°F to 780°F. Using F as the variable, write an absolute value inequality that corresponds to this range. (Modeling) Solve each problem. See Example 6. 75. Tolerance Suppose that y = 5x + 1 and we want y to be within 0.002 unit of 6. For what values of x will this be true? 49. ` 5x + 1 2 ` - 2 65 50. ` 2x + 1 3 ` + 1 64 51. 10 - 4x + 1 Ú 5 Solve each equation or inequality. See Example 4. 55. 10 - 4x Ú -4 56. 12 - 9x Ú -12 57. 6 - 3x 6 -11 58. 18 - 3x 6 -13 59. 8x + 5 = 0 60. 7 + 2x = 0 61. 4.3x + 9.8 60 62. 1.5x - 14 60 63. 2x + 1 … 0 64. 3x + 2 … 0 65. 3x + 2 70 66. 4x + 3 70 67. Concept Check Write an equation involving absolute value that says the distance between p and q is 2 units. 68. Concept Check Write an equation involving absolute value that says the distance between r and s is 6 units.
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