## Algebra 1: Common Core (15th Edition)

This statement is true when $a\gt0$
$ax\leq az$ 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 $a\gt0$