Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises - Page 167: 37


The solution is $\Big[-\dfrac{2}{3},4\Big]$

Work Step by Step

$|5-3x|\le7$ Solving this absolute value inequality is equivalent to solving the following inequality: $-7\le5-3x\le7$ $\textbf{Solve the inequality shown above:}$ $-7\le5-3x\le7$ Subtract $5$ from all three parts of the inequality: $-7-5\le5-5-3x\le7-5$ $-12\le-3x\le2$ Divide all three parts of the inequality by $-3$ and reverse the inequality signs: $\dfrac{-12}{-3}\ge\dfrac{-3x}{-3}\ge-\dfrac{2}{3}$ $4\ge x\ge-\dfrac{2}{3}$ Expressing the solution in interval notation: $\Big[-\dfrac{2}{3},4\Big]$
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