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: 96


$[-1, -\displaystyle \frac{1}{5}].$

Work Step by Step

"$ y $ is at least $6$" $\qquad $ is written as $\quad y\geq 6.$ Substituting the expression for y, $ 8-|5x+3|\geq 6\qquad $ ... add $+|5x+3|-6$ $ 2\geq|5x+3|\qquad $ ... rewrite (exchange sides, preserve direction) $|5x+3|\leq 2$ ... $|u| \leq c $ is equivalent to $\quad -c \leq u \leq c.$ $-2\leq 5x+3\leq 2\qquad $ ... add $(-3)$ $-5\leq 5x\leq-1\qquad $ ... multiply with $(\displaystyle \frac{1}{5})$ $-1\displaystyle \leq x\leq-\frac{1}{5}$ Borders are included: Solution set: $[-1, -\displaystyle \frac{1}{5}].$
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