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 - Page 118: 13

Answer

$x=\left\{ -3,\dfrac{11}{2} \right\}$

Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $ |4x-5|=17 ,$ is equivalent to \begin{array}{l}\require{cancel} 4x-5=17 \text{ OR } 4x-5=-17 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} 4x-5=17 \\\\ 4x=17+5 \\\\ 4x=22 \\\\ x=\dfrac{22}{4} \\\\ x=\dfrac{11}{2} \\\\\text{ OR }\\\\ 4x-5=-17 \\\\ 4x=-17+5 \\\\ 4x=-12 \\\\ x=-\dfrac{12}{4} \\\\ x=-3 .\end{array} Hence, the solutions are $ x=\left\{ -3,\dfrac{11}{2} \right\} .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.