Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - Chapter Review Exercises - Page 36: 3


$ x\in [-5,-1] \cup[3,7].$

Work Step by Step

$$2\leq |x-1|\leq 6\Longrightarrow 2\leq x-1\leq 6, \quad -6\leq x-1\leq -2\\ \Longrightarrow 2+1\leq x\leq 6+1, \quad 1-6\leq x\leq 1-2\\ \Longrightarrow 3\leq x\leq 7, \quad -5\leq x\leq -1.$$ So, $ x\in [-5,-1] \cup[3,7].$
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