Intermediate Algebra (6th Edition)

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

Chapter 2 - Section 2.7 - Absolute Value Inequalities - Exercise Set - Page 106: 80

Answer

$x=\left\{ -14,26 \right\}$

Work Step by Step

Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $ \left|\dfrac{6-x}{4} \right|=5 $ evaluates to \begin{array}{l} \dfrac{6-x}{4}=5\\\\ 6-x=20\\ -x=14\\ x=-14 ,\\\\\text{OR}\\\\ \dfrac{6-x}{4}=-5\\\\ 6-x=-20\\ -x=-26\\ x=26 .\end{array} Hence, the solution set is $ x=\left\{ -14,26 \right\} $.
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