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: 27


The solution is $(-4,-1)$

Work Step by Step

$|2x+5|\lt3$ Solving this absolute value inequality is equivalent to solving the following inequality: $-3\lt2x+5\lt3$ $\textbf{Solve the inequality shown above:}$ $-3\lt2x+5\lt3$ Subtract $5$ from all three parts of the inequality: $-3-5\lt2x+5-5\lt3-5$ $-8\lt2x\lt-2$ Divide all three parts of the inequality by $2$: $-\dfrac{8}{2}\lt\dfrac{2x}{2}\lt-\dfrac{2}{2}$ $-4\lt x\lt-1$ Expressing the solution in interval notation: $(-4,-1)$
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