126 Chapter 2 Linear Equations and Inequalities in One Variable Objective 1 Examples Solve each absolute value inequality. 1a. uxu < 5 1b. uy + 3u ≤ 4 1c. u2x - 1u - 5 ≤ 4 Solutions 1a. We must find all numbers whose distance from zero is less than 5. We can do this in two ways. We can write the two appropriate inequalities joined by “and” or we can write the compound inequality using the compact form. Method 1 Method 2 uxu < 5 uxu < 5 x < 5 and x > -5 -5 < x < 5 Apply property 1. Graph: –10 –8 –6 –4 –2 0 2 4 6 8 10 Interval: (-5, 5) 1b. We will solve the inequality using two separate inequalities. uy + 3u ≤ 4 y + 3 ≤ 4 and y + 3 ≥ -4 y + 3 - 3 ≤ 4 - 3 y + 3 - 3≥-4 - 3 y ≤ 1 y≥-7 Graph: –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 Interval: -7, 1 Apply property 1. Subtract 3 from each side. Simplify. 1c. We first isolate the absolute value expression and then apply property 1. We will use the compact form to solve the inequality. u2x - 1u - 5 ≤ 4 u2x - 1u - 5 + 5 ≤ 4 + 5 u2x - 1u ≤ 9 -9 ≤ 2x - 1 ≤ 9 -9 + 1 ≤ 2x - 1 + 1 ≤ 9 + 1 -8 ≤ 2x ≤ 10 -8 2x ≤ ≤ 2 2 10 2 -4 ≤ x ≤ 5 Graph: –10 –8 –6 –4 –2 0 2 4 6 8 10 Interval: -4, 5 Student Check 1 Solve each absolute value inequality. Add 5 to each side. Simplify. Apply property 1. Add 1 to each part. Simplify. Divide each part by 2. Simplify. a. uxu < 10 b. uy - 4u ≤ 5 c. u4x + 3u - 1 ≤ 6
hendricks_intermediate_algebra_1e_ch1_3
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