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: 59

Answer

$[-1,3]$

Work Step by Step

The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$ For compound inequalities, 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 change). --- $|x-1|\leq 2$ This is equivalent to $-2\leq x-1\leq 2\qquad $ ... add $1$ to all parts $-1\leq x\leq 3$ Both borders are included: The solution set is $[-1,3]$
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