Answer
$\{-1,1\}$
Work Step by Step
Recall that $|a|=b \implies a=b$ or $a=-b$.
Thus, using the rule above yields:
$-x=1\quad$ or $\quad-x=-1$
Divide both sides of both equations by $-1$.
$\dfrac{-x}{-1}=\dfrac{1}{-1}\quad$ or $\quad\dfrac{-x}{-1}=\dfrac{-1}{-1}$
Simplify.
$x=-1\quad$ or $\quad x=1$
Hence, the solution set of the given equation is $\{-1,1\}$.
