College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.5 - Solving Inequalities - 1.5 Assess Your Understanding: 8

Answer

false

Work Step by Step

RECALL: The Multiplication Properties of Inequality state that when a negative number is multiplied to each side of an inequality, the inequality sign changes to the opposite direction. Since $c$ is negative, then $\frac{1}{c}$ will also be negative. Thus, if $a\lt b$. then multiplying a negative number $\frac{1}{c}$ to each side of this inequality gives: $\begin{array}{ccc} &a &\lt &b \\&a \cdot \frac{1}{c} &\gt &b \cdot \frac{1}{c} \\&\frac{a}{c} &\gt &\frac{b}{c} \end{array}$ Therefore, the given statement is false.
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