Calculus (3rd Edition)

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

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 9: 6


$|x+2| \leq 2$

Work Step by Step

1. x belongs to the set of points from -4 to 0, with square brackets indicating that they endpoints are included. This can be rewritten as: $-4 \leq x \leq 0$ 2. In order to express this in terms of an inequality, we must show that: $|x−c| \leq r$ and $c−r \leq x \leq c+r$ 3. By combining steps one and two: $c−r=-4$, and $c+r=0$ 4. In order to satisfy those equations: $c=-2$, and $r=2$ Therefore: $|x+2| \leq 2$
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