Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 2 - Section 2.7 - Linear Inequalities and Problem Solving - Exercise Set: 85

Answer

The direction of the inequality symbol is reversed when you multiply or divide an inequality by a negative number.

Work Step by Step

Take the inequality: $ 5 \lt 20$ as an eample. When multiplying the inequality by $-1$, $-5 \lt -20$. This is false as -5 should be greater than -20. So this is only true when the inequality sign is reversed. $-5 \gt -20$ A larger magnitude of a positive value is larger than a smaller magnitude of a positive value. However, a smaller magnitude of a negative value is larger than a larger magnitude of a negative value. Hence, the inequality sign is reversed when multiplying or dividing by a negative value. See "question 84" as another example.
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