College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Section 1.7 - Solving Inequalities - 1.7 Exercises - Page 148: 46


The solution set is $(-\infty,-3]\cup[3,\infty)$

Work Step by Step

$x^2\ge9\hspace{0.7cm}{\color{blue}{\text{Given equation}}}$ $\Rightarrow x^2-9\ge0$ $\Rightarrow (x-3)(x+3)\ge0\hspace{0.7cm}{\color{blue}{\text{Factor}}}$ The factors of the left-hand side are $x-3$ and $x+3$. These factors are zero when $x=3$ and $x=-3$. These numbers divide the real line into the intervals $(-\infty,-3),(-3,3),(3,\infty)$ From the diagram and hence the inequality involves $\ge$, the endpoints of the intervals satisfy the inequality. The solution set is $(-\infty,-3]\cup[3,\infty)$
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