Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 98


$[-2,-\displaystyle \frac{2}{9}]$

Work Step by Step

4 times a number is subtracted from 5 can be written as: $5-4x $ The absolute value of the difference $|5-4x|$ is at most 13: $|5-4x|\leq 13$ $|5-4x|=|4x-5| \qquad $, because $|a-b|=|b-a|$ So, we solve $|4x-5|\leq 13$ $|u| \leq c $ is equivalent to $-c \leq u \leq c.$ $-13\leq 4x-5\leq 13\qquad.../+5$ $-8\leq 4x\leq 18 \qquad.../\div 4$ $-2\displaystyle \leq x\leq\frac{9}{2}$ Borders are included: Solution set: $[-2,-\displaystyle \frac{2}{9}]$
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