Section 1.7 Absolute Value Inequalities 109 Answers 9. 10. 11. ƒ x 4 ƒ 6 6 1, 182´ 12, 2 ƒ x ƒ 7 10 Test t 0 Test t 10 Test t 16 : : : 1102 5 ` 3 ? 1 ` 1 1 3 1 ` ? 3 1162 5 ` ? 3 1 0 00 5 3 1 05 5 0 ? 3 1 08 0 ? ? 5 1 03 0 3 ? 1 00 0 3 ? 1 05 0 3 ? 4 True 3 ? 1 False 3 ? 6 True Step 4: The original inequality uses the sign .Therefore, the boundary points (where equality occurs) must be part of the solution set. True False True 6 14 5t 0 t 6 or t 146 The solution is or, equivalently in interval notation, 1, 6 4 ´ 314, 2. Skill Practice Solve the inequality. 9. ` 1 2 c 4 ` 1 7 6 3 ? 1 ` 1 2 2 2 102 5 ` 3. Translating to an Absolute Value Expression Absolute value expressions between c and d is given by 0c can 0 be used to describe distances. The distance 0 122 0 d 0. For 0 example, the distance between 2 and 3 on the number line is 3 5 5 as expected. Expressing Distances with Absolute Value Example 7 Write an absolute value inequality to represent the following phrases. a. All real numbers x, whose distance from zero is greater than 5 units b. All real numbers x, whose distance from 7 is less than 3 units Solution: a. All real numbers x, whose distance from zero is greater than 5 units 5 units 5 units ( ( 6 54 3 2 1 0 1 2 3 4 5 6 0x 0 0 7 5 or simply 0x 0 7 5 b. All real numbers x, whose distance from is less than 3 units 3 units 3 units ( ( 7 11109 8 7 6 5 4 3 2 0x 172 0 6 3 or simply 0x 7 0 6 3 Skill Practice Write an absolute value inequality to represent the following phrases. 10. All real numbers whose distance from zero is greater than 10 units 11. All real numbers whose distance from 4 is less than 6 units
miller_intermediate_algebra_4e_ch1_3
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