College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Test - Page 168: 28

Answer

$\left( -2,7 \right)$

Work Step by Step

Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$, then the solution to the given inequality, $ \left| 2x-5 \right|\lt9 ,$ is \begin{array}{l}\require{cancel} -9\lt 2x-5\lt9 \\\\ -9+5\lt 2x-5+5\lt9+5 \\\\ -4\lt 2x\lt14 \\\\ -\dfrac{4}{2}\lt \dfrac{2x}{2}\lt\dfrac{14}{2} \\\\ -2\lt x\lt7 .\end{array} Hence, the solution set is the interval $ \left( -2,7 \right) .$
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