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 274: 78

Answer

We solve the inequalities and graph the results on a number line.

Work Step by Step

In order to solve an inequality involving the word "and" (as opposed to "or"), we solve each inequality separately, graph each resulting inequality, and graph the overlapping solution set. In general, two "and" inequalities such as: $a \lt x$ and $x \lt b$ can be combined into one inequality as: $ a \lt x \lt b$ This can be done as long as $a \lt b$. If necessary, we would then solve for (isolate) $x$ in the middle. Finally, we would graph the solution on the number line.
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