Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 179: 93

Answer

$(-\infty, -4]\cup[0,4]$

Work Step by Step

Step 1. Factor the inequality to get $x(x+4)(x-4)\leq0$ Step 2. Identify the boundary points $x=-4, 0, 4$ and separate the number line into intervals $(-\infty, -4)$, $(-4,0)$, $(0,4)$ and $(4,\infty)$ Step 3. Use test points $x=-5,-1,1,5$ to get the signs of the left side of the inequality as $-,+,-,+$ Step 4. Based on the signs and consider the boundary points for the equal sign, we have the solution as $(-\infty, -4]\cup[0,4]$
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