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 94: 31


$\left[ -\dfrac{7}{3},7 \right]$

Work Step by Step

Using properties of inequality, then, \begin{array}{l} -5\le \dfrac{-3x+1}{4}\le2\\\\ -5\cdot4\le \dfrac{-3x+1}{4}\cdot4\le2\cdot4\\\\ -20\le -3x+1\le8\\\\ -20-1\le -3x+1-1\le8-1\\\\ -21\le -3x\le7\\\\ 7\ge x\ge-\dfrac{7}{3}\\\\ -\dfrac{7}{3}\le x\le7 .\end{array} Hence, the solution set is $ \text{ the interval } \left[ -\dfrac{7}{3},7 \right] $.
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