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: 79

Answer

$x=\left\{ -\dfrac{17}{2},\dfrac{19}{2} \right\}$

Work Step by Step

Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $ \left|\dfrac{2x-1}{3} \right|=6 $ evaluates to \begin{array}{l} \dfrac{2x-1}{3}=6\\\\ 2x-1=18\\ 2x=19\\\\ x=\dfrac{19}{2} ,\\\\\text{OR}\\\\ \dfrac{2x-1}{3}=-6\\\\ 2x-1=-18\\ 2x=-17\\\\ x=-\dfrac{17}{2} .\end{array} Hence, the solution set is $ x=\left\{ -\dfrac{17}{2},\dfrac{19}{2} \right\} $.
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