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: 2


(a) $ x\in(1,9)$ (b) $ x\in[-1,-1/5]$.

Work Step by Step

(a) $$|x-5|\lt 4\Longrightarrow 5-4\lt x\lt 4+5 \Longrightarrow 1\lt x\lt 9.$$ So, $ x\in(1,9)$ (b) $$|5x+3|\leq 2\Longrightarrow -3-2\leq 5x\leq 2-3 \\ \Longrightarrow -5\leq 5x\leq -1\Longrightarrow -1\leq x\leq -1/5.$$ So, $ x\in[-1,-1/5]$.
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