Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 162: 93

Answer

$(-\infty,-2]U[0,2]$

Work Step by Step

Step 1. Factor the left side to get $x(2+x)(2-x)\ge0$, then identify the boundary points at $x=-2, 0,2$ Step 2. Plot the above points on a number line and obtain four intervals $(-\infty,-2],[-2,0],[0,2],[2,\infty)$ Step 3. Choose test values at $x=-3,-1,1,3$ for each interval and test the inequality. The results are $T, F,T,F$ (T for True, F for False) for each interval. Step 4. The solutions are the intervals with true results: $(-\infty,-2]U[0,2]$
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