#### Answer

False.
It is true only if $c\geq0$

#### Work Step by Step

$a\leq b$
If $c$ is positive:
$ac\leq bc$
If $c$ is negative, then $-c$ is positive:
$a(-c)\leq b(-c)$
$-ac\leq -bc$
$ac\geq bc$
If $c=0$:
$a(0)=b(0)$
See Property 4 on page 132.