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: 63


$[-5, 3]$

Work Step by Step

The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$ The idea is to isolate $x$ in the middle. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain). Multiplying/dividing with a negative number inverts the order (the inequality symbols changes). --- $|2(x-1)+4|\leq 8\qquad $... is equivalent to ... $-8\leq 2(x-1)+4\leq 8 \qquad $ ... simplify the middle $-8\leq 2x-2+4\leq 8$ $-8\leq 2x+2\leq 8\qquad $ ... add $-2$ to all parts $-10\leq 2x\leq 6\qquad $ ... divide with $2$ $-5\leq x\leq 3$ Interval borders are included in the interval. The solution set is $[-5, 3].$
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