Intermediate Algebra (6th Edition)

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

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 95: 52


$\left( \dfrac{1}{6},\dfrac{7}{2} \right)$

Work Step by Step

Using the properties of inequality, the solution set of the given inequality, $ \dfrac{2}{3}\lt x+\dfrac{1}{2}\lt4 ,$ is \begin{array}{l}\require{cancel} \dfrac{2}{3}-\dfrac{1}{2}\lt x+\dfrac{1}{2}-\dfrac{1}{2}\lt4-\dfrac{1}{2} \\\\ \dfrac{4}{6}-\dfrac{3}{6}\lt x\lt\dfrac{8}{2}-\dfrac{1}{2} \\\\ \dfrac{1}{6}\lt x\lt\dfrac{7}{2} .\end{array} Hence, the solution set is $ \left( \dfrac{1}{6},\dfrac{7}{2} \right) .$
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