Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 1 - Section 1.7 - Absolute Value Equations and Inequalities - 1.7 Exercises: 21


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

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |0.5x|=6 ,$ is equivalent to \begin{array}{l}\require{cancel} 0.5x=6 \text{ OR } 0.5x=-6 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 0.5x=6 \\\\ 10(0.5x)=(6)10 \\\\ 5x=60 \\\\ x=\dfrac{60}{5} \\\\ x=12 \\\\\text{ OR }\\\\ 0.5x=-6 \\\\ 10(0.5x)=(-6)10 \\\\ 5x=-60 \\\\ x=-\dfrac{60}{5} \\\\ x=-12 .\end{array} Hence, the solutions are $ x=\left\{ -12,12 \right\} .$
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