Answer
$\{-1,2\}$
Work Step by Step
Recall that $|a|=b \implies a=b$ or $a=-b$.
Thus, using the rule above yields:
$1-2z=3\quad $ or $\quad1-2z=-3$
Subtract $1$ from both sides of both equations.
$1-2z-1=3-1\quad$ or $\quad1-2z-1=-3-1$
Simplify.
$-2z=2\quad $ or $\quad -2z=-4$
Divide both sides of both equations by $-2$.
$\dfrac{-2z}{-2}=\dfrac{2}{-2}\quad$ or $\quad\dfrac{-2z}{-2}=\dfrac{-4}{-2}$
Simplify.
$z=-1\quad$ or $\quad z=2$
Hence, the solution set of the given equation is $\{-1,2\}$.
