Intermediate Algebra (12th Edition)

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

Chapter 1 - Review Exercises: 63

Answer

$x=\left\{ -\dfrac{1}{3}, 5 \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given equation, $ |3x-7|=8 ,$ is equivalent to \begin{array}{l}\require{cancel} 3x-7=8 \text{ OR } 3x-7=-8 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 3x-7=8 \\\\ 3x=8+7 \\\\ 3x=15 \\\\ x=\dfrac{15}{3} \\\\ x=5 \\\\\text{ OR }\\\\ 3x-7=-8 \\\\ 3x=-8+7 \\\\ 3x=-1 \\\\ x=-\dfrac{1}{3} .\end{array} Hence, the solutions are $ x=\left\{ -\dfrac{1}{3}, 5 \right\} .$
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