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: 32


The solution is $\Big(-\dfrac{8}{5},\dfrac{2}{5}\Big)$

Work Step by Step

$\Big|\dfrac{3}{5}+x\Big|\lt1$ Solving this absolute value inequality is equivalent to solving the following inequality: $-1\lt\dfrac{3}{5}+x\lt1$ Multiply the whole inequality by $5$: $5\Big(-1\lt\dfrac{3}{5}+x\lt1\Big)$ $-5\lt3+5x\lt5$ Subtract $3$ from all three parts of the inequality: $-5-3\lt3-3+5x\lt5-3$ $-8\lt5x\lt2$ Divide all three parts of the inequality by $5$: $-\dfrac{8}{5}\lt\dfrac{5x}{5}\lt\dfrac{2}{5}$ Expressing the solution in interval notation: $\Big(-\dfrac{8}{5},\dfrac{2}{5}\Big)$
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