Answer
See below.
Work Step by Step
Case1: if $r=0$, we have $|r|=0\le c$;
Case2: if $r\gt0$, we have $|r|=r\le c$;
Case3: if $r\lt0$, we have $|r|=-r$, since $-c\le r$, we have $c\ge -r$, thus $|r|=-r\le c$;
Based on the above, in any case of $r$, we have $|r|\le c$.