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 - Concept and Vocabulary Check - Page 137: 10

Answer

$-2\lt x-7 \lt 2$

Work Step by Step

Solving an Absolute VaIue Inequality: If $ u $ is an algebraic expression and $ c $ is a positive number, then: 1) The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$ 2) The solutions of $|u|\gt c $ are the numbers that satisfy $ u\lt -c $ or $ u\gt c.$ These rules are valid if $ \lt$ is replaced by $\leq $ and $ \gt \mathrm{i}\mathrm{s}$ replaced by $\geq.$ --- Apply case 1: $-2\lt x-7 \lt 2$
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