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 - Cumulative Review Exercises - Page 311: 18

Answer

$(-\infty,3]\cup[5,\infty)$. The graph of the solution set is shown below.

Work Step by Step

The given compound inequality is $x-4\geq1$ or $-3x+1\geq-5-x$. Solve each inequality separately. First $x-4\geq1$. Add $4$ to both sides. $\Rightarrow x-4+4\geq1+4$ Simplify. $\Rightarrow x\geq5$ Second $-3x+1\geq-5-x$. Add $x-1$ to both sides. $\Rightarrow -3x+1+x-1\geq-5-x+x-1$ Simplify. $\Rightarrow -2x\geq-6$ Divide both sides $-2$ and change the sense of inequality. $\Rightarrow \frac{-2x}{-2}\leq\frac{-6}{-2}$ Simplify. $\Rightarrow x\leq3$ First graph then take the union of the two inequalities. We can write the compound inequality. $x\geq5$ as $[5,\infty)$ or $x\leq3$ as $(-\infty,3]$ The union is $(-\infty,3]\cup[5,\infty)$. The combined graph is shown below.
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