Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Review - Page 113: 97


$x=\left\{ -3,3 \right\}$

Work Step by Step

Using the properties of equality, the given expression, $ \left| 7x \right|-26=-5 ,$ is equivalent to \begin{array}{l}\require{cancel} \left| 7x \right|=-5+26 \\\\ \left| 7x \right|=21 .\end{array} Since for any $a\gt0$, $|x|=a$ implies $x=a\text{ or } x=-a$, then the expression, $ \left| 7x \right|=21 ,$ is equivalent to \begin{array}{l}\require{cancel} 7x=21 \\\\ x=\dfrac{21}{7} \\\\ x=3 ,\\\\\text{ OR }\\\\ 7x=-21 \\\\ x=-\dfrac{21}{7} \\\\ x=-3 .\end{array} Hence, the solution set is $ x=\left\{ -3,3 \right\} .$
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