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: 28

Answer

The solution is $\Big(\dfrac{2}{3},2\Big)$

Work Step by Step

$|3x-4|\lt2$ Solving this absolute value inequality is equivalent to solving the following inequality: $-2\lt3x-4\lt2$ $\textbf{Solve the inequality shown above:}$ $-2\lt3x-4\lt2$ Add $4$ to all three parts of the inequality: $-2+4\lt3x-4+4\lt2+4$ $2\lt3x\lt6$ Divide all three parts of the inequality by $3$: $\dfrac{2}{3}\lt\dfrac{3x}{3}\lt\dfrac{6}{3}$ $\dfrac{2}{3}\lt x\lt2$ Expressing the solution in interval notation: $\Big(\dfrac{2}{3},2\Big)$
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