Answer
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 $a\gt0$
