College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises: 108

Answer

$\color{blue}{(-\infty, -5.099] \cup [-2.499, 2.499] \cup [5.099, +\infty)}$ Refer to the image below for the graph.
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Work Step by Step

To solve the given inequality graphically, perform the following steps: (1) Let the left side the inequality represent a function then graph using a graphing utility. Graph $y=|x^2-16|=10$. (refer to the attached image in the answer part above for the graph) (2) Identify the region/s where graph is above the x-axis. Note that the graph is above the x-axis in the following intervals: $(-\infty, -5.099)$, $(-2.499, 2.499)$, and $(5.099, +\infty)$ This means that the value of $|x^2-16|-10$ is greater than or equal to 0 in the intervals $(-\infty, -5.099)$, $(-2.499, 2.499)$, and $(5.099, +\infty)$. Since the inequality involves $\ge$, then the endpoints $-5.099, -2.499, 2.499,$ and $5.099$ are part of the solution set. Therefore, the solution set is: $\color{blue}{(-\infty, -5.099] \cup [-2.499, 2.499] \cup [5.099, +\infty)}$
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