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: 30

Answer

The solution is $\Big(-\infty,\dfrac{2}{3}\Big]\cup\Big[2,\infty\Big)$

Work Step by Step

$|3x-4|\ge2$ Solving this absolute value inequality is equivalent to solving two separate inequalities, which are: $3x-4\ge2$ and $3x-4\le-2$ $\textbf{Solve the first inequality:}$ $3x-4\ge2$ Take $4$ to the right side: $3x\ge2+4$ $3x\ge6$ Take $3$ to divide the right side: $x\ge\dfrac{6}{3}$ $x\ge2$ $\textbf{Solve the second inequality:}$ $3x-4\le-2$ Take $4$ to the right side: $3x\le-2+4$ $3x\le2$ Take $3$ to divide the right side: $x\le\dfrac{2}{3}$ $\Big(-\infty,\dfrac{2}{3}\Big]\cup\Big[2,\infty\Big)$
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