Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 24


The solution is $[-4,\infty)$

Work Step by Step

$-\dfrac{2}{3}x-\dfrac{1}{6}x+\dfrac{2}{3}(x+1)\le\dfrac{4}{3}$ Multiply the whole inequality by $6$: $6\Big[-\dfrac{2}{3}x-\dfrac{1}{6}x+\dfrac{2}{3}(x+1)\le\dfrac{4}{3}\Big]$ $-2(2)x-x+2(2)(x+1)\le4(2)$ $-4x-x+4x+4\le8$ Simplify the left side: $-x+4\le8$ Take $4$ to the right side: $-x\le8-4$ $-x\le4$ Rearrange: $x\ge-4$ Expressing the solution in interval notation: $[-4,\infty)$
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