Absolute Value Equations and Inequalities

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Absolute Value Equations and Inequalities Practice 1 - 5 Absolute Value Equations and Inequalities Write each specification as an absolute value inequality. 6.3 ≤ h ≤ 10.3 Mid point of the interval is (10.3+6.3)/2 = 16. 6/2 = 8.3 Distance to endpoints is 10.3 - 8.3 = 2 Absolute Value is: |h - 8.3| ≤ 2 2. - 2.5 ≤ a ≤ 2.5 Here midpoint is 0. Distance to endpoints is 2.5 – 0 = 2.5 Therefore, absolute value is |a| ≤ 2.5 3. 22 ≤ x ≤ 33 Midpoint is (33+22)/2 = 27.5 Distanc e is 33 – 27.5 = 5.5 Therefore, absolute value is |x – 27.5|≤5.5 Solve each inequality. Graph the solutions. 4. 5 + x >12 Break up the absolute value x + 5 < - 12 and x + 5 > 12 x + 5 < - 12 …………… Subtract 5 from both sides x + 5 – 5 < - 12 – 5 x < - 17 Now lets focus on the second inequality x + 5 > 12 Subtract 5 from both sides x + 5 – 5 > 12 – 5
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x > 7 Therefore answer is x < - 17 or x > 7 5. 3 − k ≤ 19 Break up the absolute value k - 3 ≤ 19 and k - 3 ≥ - 19 k - 3 ≤ 19 …………… Add 3 from both sides k – 3 + 3 ≤ 19 + 3 k ≤ 22 Now lets focus on the second inequality k - 3 ≥ - 19 Add 3 from both sides k - 3 + 3 ≥ - 19 + 3 k ≥ - 16 Therefore answer is k ≤ 22 or k ≥ - 16 or - 16 ≤ k ≤ 22 6. 2 + x ≥ 0 Solution for this equation is all real numbers . 7. 2 5 − t <14 Divide both sides with 2. 5 − t <14/2 = = > 5 − t <7 Break up the absolute value t - 5 < 7 and t - 5 > - 7 t - 5 < 7 …………… Add 5 from both sides t – 5 + 5 < 7 + 5 t < 12 Now lets focus on the second inequality t - 5 > - 7 Add 5 from both sides t - 5 + 5 > - 7 + 5

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