104 Chapter 1 Linear Equations and Inequalities in One Variable 0x 0 7 3 0x 0 6 3 Solution: The set of all points more than 3 units from zero 3. Solution: ( ( 1 2 3 4 5 6 3 6 x 6 3 The set of all points less than 3 units from zero ( ( 1 2 3 4 5 6 3 units 6 5 4 3 2 1 0 3 units 3 units 6 5 4 3 2 1 0 3 units 2. x 6 3 or x 7 3 Solving Absolute Value Equations and Inequalities Let a be a real number such that Then Equation/ Solution Inequality (Equivalent Form) Graph 0x 0 x a or x a a 0x 0 7 a x 6 a or x 7 a To solve an absolute value inequality, first isolate the absolute value and then rewrite the absolute value inequality in its equivalent form. Solving an Absolute Value Inequality Example 1 Solve the inequality. Solution: 03w 1 0 4 6 7 Isolate the absolute value first. The inequality is in the form , where x 3w 1. 0x 0 6 a 3w 1 0 4 6 7 03w 1 0 6 11 0 11 6 3w 1 6 11 a 6 x 6 a. Rewrite in the equivalent form Solve for w. 12 6 3w 6 10 4 6 w 6 10 3 6 54 3 2 1 0 1 2 3 4 5 6 5w 0 4 6 w 6 10 ( ( 3 6 10 3 The solution is , or equivalently in interval notation, . 14, 10 3 2 Skill Practice Solve the inequality. Write the solution in interval notation. 1. ƒ 2t 5 ƒ 2 11 TIP: Recall that a strict inequality (using the symbols > and <) will have parentheses at the endpoints of the interval form of the solution. Answer 1. 37, 2 4 a a ( ( a a ( ( a a 0x 0 6 a a 6 x 6 a a 7 0.
miller_intermediate_algebra_4e_ch1_3
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