Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.8 - Inequalities - 1.8 Exercises - Page 89: 80


$\left( -\infty, -2 \right] \cup \left[ 0,\infty \right)$

Work Step by Step

For any $a\gt0$, $|x|\gt a$ implies $x\gt a \text{ OR } x\lt -a$. (The symbol $\gt$ may be replaced with $\ge$.) Using the concept above, the solutions to the given inequality, $ |x+1|\ge1 ,$ is \begin{array}{l}\require{cancel} x+1\ge1 \\\\ x\ge1-1 \\\\ x\ge0 ,\\\\\text{ OR }\\\\ x+1\le-1 \\\\ x\le-1-1 \\\\ x\le-2 .\end{array} In interval notation, the solution set is $ \left( -\infty, -2 \right] \cup \left[ 0,\infty \right) .$
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