What are the real solutions to the equation $|1-2x|=3 $ ?

$x=-1$ only

$x=-1$ and $x=-2$

$x=-1$ and $x=1$

$x=-1$ and $x=2$

$x=1$ and $x=-2$

Approach 1

$|-3| \text{ and } |3| $ both equal $3$, so

$1-2x=3$

$$ -2x=2 $$ $$ x=-1$$

$1-2x=-3$

$$ -2x=-4 $$ $$ x=2 $$

$$ x=-1 \text{ and } x=2 $$

Approach 2

Plug in the answer choices.