98 Chapter 1 Linear Equations and Inequalities in One Variable Answers 1. 2. 3. 506 4. 5 6 57, 76 54, 46 To solve an absolute value equation of the form rewrite the equation as x a or x a. Solving Absolute Value Equations Solve the absolute value equations. a. 0x 0 5 b. 0w0 2 12 c. 0 p 0 0 d. 0x 0 6 Solution: a. 0x 0 5 The equation is in the form 0x 0 a, where x 5 or x 5 Rewrite the equation as x a or x a. The solution set is . b. Isolate the absolute value to write the equation in the form 0w0 14 w 14 or w 14 Rewrite the equation as w a or w a. The solution set is 514, 146. 0 x 0 a. 0w0 2 12 55, 56 a 5. Example 1 0x 0 a 1a 02, c. Rewrite as two equations. Notice that the second equation p 0 is the same as the first equation. Intuitively, p 0 is the only number whose absolute value equals 0. 0p 0 0 p 0 or p 0 The solution set is 506. 0x 0 0x 0 a, 6 d. The equation is of the form but a is negative. There is no number whose 5 6 No solution, absolute value is negative. Skill Practice Solve the absolute value equations. 1. 2. 3. 4. 0z 0 0w 0 12 0v 0 0 0y 0 6 10 7 We have solved absolute value equations of the form Notice that x can represent any algebraic quantity. For example, to solve the equation we still rewrite the absolute value equation as two equations. In this case, we set the quantity 2w 3 equal to 5 and to 5, respectively. 02w 3 0 5 2w 3 5 or 2w 3 5 02w 3 0 5, 0x 0 a.
miller_intermediate_algebra_4e_ch1_3
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