College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Review Exercises - Page 166: 121


$x=\left\{ -4,-\dfrac{2}{3} \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the given inequality, $ \left| 3x+7 \right|-5=0 ,$ is equivalent to \begin{array}{l}\require{cancel} \left| 3x+7 \right|=5 \\\\ 3x+7=5 \\\text{ OR }\\ 3x+7=-5 .\end{array} Solving each equation separately, then, \begin{array}{l}\require{cancel} 3x+7=5 \\\\ 3x=5-7 \\\\ 3x=-2 \\\\ x=-\dfrac{2}{3} \\\text{ OR }\\ 3x+7=-5 \\\\ 3x=-5-7 \\\\ 3x=-12 \\\\ x=-\dfrac{12}{3} \\\\ x=-4 .\end{array} Hence, $ x=\left\{ -4,-\dfrac{2}{3} \right\} .$
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