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: 48

Answer

The solution is $\Big(-\dfrac{7}{5},\dfrac{3}{5}\Big)$

Work Step by Step

$|5x+2|-2\lt3$ Take $2$ to the right side of the inequality: $|5x+2|\lt3+2$ $|5x+2|\lt5$ Solving this absolute value inequality is equivalent to solving the following inequality: $-5\lt5x+2\lt5$ $\textbf{Solve the inequality shown above:}$ $-5\lt5x+2\lt5$ Subtract $2$ from all three parts of the inequality: $-5-2\lt5x+2-2\lt5-2$ $-7\lt5x\lt3$ Divide all three parts of the inequality by $5$: $-\dfrac{7}{5}\lt\dfrac{5x}{5}\lt\dfrac{3}{5}$ $-\dfrac{7}{5}\lt x\lt\dfrac{3}{5}$ Expressing the solution in interval notation: $\Big(-\dfrac{7}{5},\dfrac{3}{5}\Big)$
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