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: 14


$x=\left\{ -4,\dfrac{22}{5} \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |5x-1|=21 ,$ is equivalent to \begin{array}{l}\require{cancel} 5x-1=21 \text{ OR } 5x-1=-21 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 5x-1=21 \\\\ 5x=21+1 \\\\ 5x=22 \\\\ x=\dfrac{22}{5} \\\\\text{ OR }\\\\ 5x-1=-21 \\\\ 5x=-21+1 \\\\ 5x=-20 \\\\ x=-\dfrac{20}{5} \\\\ x=-4 .\end{array} Hence, the solutions are $ x=\left\{ -4,\dfrac{22}{5} \right\} .$
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