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 - Test - Page 310: 8

Answer

$(-\infty,4)$. The graph of the solution set is shown below.

Work Step by Step

The given compound inequality is $2x-3\lt5$ or $3x-6\leq4$. Solve each inequality separately. First $=2x-3\lt5$. Add $3$ to both sides. $=2x-3+3\lt5+3$ Simplify. $=2x\lt8$ Divide both sides by $2$. $=\frac{2x}{2}\lt\frac{8}{2}$ Simplify. $=x\lt4$ Second $=3x-6\leq4$. Add $6$ to both sides. $=3x-6+6\leq4+6$ Simplify. $=3x\leq10$ Divide both sides by $3$. $=\frac{3x}{3}\leq\frac{10}{3}$ Simplify. $=x\leq\frac{10}{3}$ First graph then take the union of the two inequality. We can write the compound inequality. $x\lt4$ as $(-\infty,4)$ and $x\leq\frac{10}{3}$ as $(-\infty,\frac{10}{3}]$ The union is $(-\infty,4)\cup(-\infty,\frac{10}{3}]=(-\infty,4)$. The combined graph is shown in the image file.
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