Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 3 - Solving Inequalities - 3-3 Solving Inequalities Using Multiplication or Division - Practice and Problem-Solving Exercises - Page 183: 62


This statement is true when $a\gt0$

Work Step by Step

$ax\leq az$ Divide both sides by a: $\frac{ax}{a}\leq\frac{az}{a}$ $x\leq z$ If $a\lt0$: $ax\leq az$ $\frac{ax}{a}\leq\frac{az}{a}$ $x\leq z$ (Reverse inequality because a is negative) This lets us conclude that $x\leq z$ is only true when $a\gt0$ for this situation The statement is true when $a\gt0$
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