Intermediate Algebra (12th Edition)

Published by Pearson

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 19

Answer

$x=\left\{ 12,36 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $\left|12-\dfrac{1}{2}x\right|=6 ,$ is equivalent to \begin{array}{l}\require{cancel} 12-\dfrac{1}{2}x=6 \text{ OR } 12-\dfrac{1}{2}x=-6 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 12-\dfrac{1}{2}x=6 \\\\ -\dfrac{1}{2}x=6-12 \\\\ -\dfrac{1}{2}x=-6 \\\\ -2\left(-\dfrac{1}{2}x\right)=(-6)(-2) \\\\ x=12 \\\\\text{ OR }\\\\ 12-\dfrac{1}{2}x=-6 \\\\ -\dfrac{1}{2}x=-6-12 \\\\ -\dfrac{1}{2}x=-18 \\\\ -2\left(-\dfrac{1}{2}x\right)=(-18)(-2) \\\\ x=36 .\end{array} Hence, the solutions are $x=\left\{ 12,36 \right\} .$

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