I'm looking find all $c \in \mathbb{R}$ that solve the inequality:

$cx \leq |x|$, for all $x \in \mathbb{R}$

I know the solution should be $-1 \leq c \leq 1$, but don't know how I am supposed to get there.

Could someone walk me through how to navigate the absolute value when there is an x outside the absolute value?