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: 31

Answer

The solution is $\Big(-\dfrac{3}{2},\dfrac{5}{2}\Big)$

Work Step by Step

$\Big|\dfrac{1}{2}-x\Big|\lt2$ Solving this absolute value inequality is equivalent to solving the following inequality: $-2\lt\dfrac{1}{2}-x\lt2$ Multiply the whole inequality by $-2$: $-2\Big(-2\lt\dfrac{1}{2}-x\lt2\Big)$ $4\gt-1+2x\gt-4$ Add $1$ to all three parts of the inequality: $4+1\gt-1+1+2x\gt-4+1$ $5\gt2x\gt-3$ Divide all three parts of the inequality by $2$: $\dfrac{5}{2}\gt\dfrac{2x}{2}\gt-\dfrac{3}{2}$ $\dfrac{5}{2}\gt x\gt-\dfrac{3}{2}$ Expressing the solution in interval notation: $\Big(-\dfrac{3}{2},\dfrac{5}{2}\Big)$
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