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.
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