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Absolute Value Equations and Inequalities

A set of algebraic problems focusing on absolute value equations and inequalities.

Benjamin Clark
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Absolute Value Equations and InequalitiesPractice 1-5Absolute Value Equations and InequalitiesWrite each specification as an absolute value inequality.6.3 ≤h≤ 10.3Mid pointof the intervalis (10.3+6.3)/2 = 16.6/2 = 8.3Distance to endpointsis10.3-8.3 = 2Absolute Value is:|h-8.3| ≤ 22.-2.5 ≤ a≤2.5Here midpoint is 0.Distance to endpoints is 2.5–0 = 2.5Therefore, absolute value is|a|≤ 2.53.22≤x≤33Midpoint is (33+22)/2 = 27.5Distance is 33–27.5 = 5.5Therefore, absolute value is|x–27.5|≤5.5Solve each inequality. Graph the solutions.4.5+x>12Break up the absolute value x + 5 <-12 and x + 5 > 12x + 5 <-12……………Subtract 5 from both sidesx + 5–5 <-12–5x <-17Now lets focus on the secondinequalityx + 5 > 12Subtract 5 from both sidesx + 5–5 > 12–5

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