76 Chapter 1 Linear Equations and Inequalities in One Variable 55. 56. 57. 3x 3y 6 2x 2y 8 y 5 2 3 1 3 9x 58. 4x 59. y 0 60. x x m 4 3 1 4 x y 0 y 5 In statistics, the z-score formula z is used in studying probability. Use this formula for Exercises 61–62. s x m 62. a. Solve for z m. s b. Find m when x 150, z 2.5, and s 16. 64. Which expressions are equivalent to z 1 2 1 z 2 z 1 2 a. b. c. 66. Which expressions are equivalent to 3w x y 3w 3w x y a. b. c. x y x m 61. a. Solve z for x. s b. Find x when z 2.5, m 100, and s 12. 63. Which expressions are equivalent to 5 3 x 5 x 3 5 x 3 a. b. c. ? 5 x 3 65. Which expressions are equivalent to x 7 y x 7 y x 7 a. b. c. y ? x 7 y For Exercises 67–75, solve for the indicated variable. (See Example 6.) 67. 68. 69. ? z 1 2 ? 3w x y 6t rt 12 for t 5 4a ca for a ax 5 6x 3 for x cx 4 dx 9 for x A P Prt for P A P Prt for r 70. 71. 72. 73. T mg mf for m 74. T mg mf for f 75. ax by cx z for x Section 1.4 Linear Inequalities in One Variable 1. Solving Linear Inequalities In Sections 1.1–1.3, we learned how to solve linear equations and their applications. In this section, we will learn the process of solving linear inequalities. A linear inequality in one variable, x, is defined as any relationship of the form: ax b 6 c, ax b c, ax b 7 c, or ax b c, where a 0. The solution to the equation can be graphed as a single point on the 5 4 3 2 1 0 1 2 3 4 5 number line. x 3 Concepts 1. Solving Linear Inequalities 2. Applications of Inequalities
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