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: 39

Answer

The solution set is $(-\infty,-1]\cup[\frac{1}{2},\infty)$

Work Step by Step

$2x^2+x\ge1\hspace{0.7cm}{\color{blue}{\text{Given equation}}}$ $\Rightarrow 2x^2+x-1\ge0$ $\Rightarrow (2x-1)(x+1)\ge0\hspace{0.7cm}{\color{blue}{\text{Factor}}}$ The factors of the left-hand side are $2x-1$ and $x+1$. These factors are zero when $x=\frac{1}{2}$ and $x=-1$. These numbers divide the real line into the intervals $(-\infty,-1),(-1,\frac{1}{2}),(\frac{1}{2},\infty)$ From the diagram and hence the inequality involves $\ge$, the endpoints of the intervals satisfy the inequality. The solution set is $(-\infty,-1]\cup[\frac{1}{2},\infty)$
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