Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 4 - Section 4.2 - Compound Inequalities - Exercise Set - Page 272: 20

Answer

$(-2,\frac{5}{2})$. The graph is shown below.

Work Step by Step

The given compound inequality is $6-5x\gt1-3x$ and $4x-3\gt x-9$. Solve each inequality separately. $\Rightarrow 6-5x\gt1-3x$ and $4x-3\gt x-9$. $\Rightarrow 6\gt1-3x+5x$ and $4x-3-x\gt -9$. $\Rightarrow 6\gt1+2x$ and $3x-3\gt -9$. $\Rightarrow 6-1\gt2x$ and $3x\gt -9+3$. $\Rightarrow 5\gt2x$ and $3x\gt -6$. $\Rightarrow \frac{5}{2}\gt x$ and $x\gt -2$. First graph then take the intersection of the solution sets of the two inequalities.. The graph is shown in the image file. We can write the compound inequality. $\frac{5}{2}\gt x$ as $(-\infty,\frac{5}{2})$ and $x\gt-2$ as $(-2,\infty)$ The intersection is $(-\infty,\frac{5}{2})\cap(-2,\infty)=(-2,\frac{5}{2})$.
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