#### Answer

The solution is $x=2$

#### Work Step by Step

$|3-2x|=|5-2x|$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$3-2x=5-2x$ and $3-2x=-(5-2x)$
$\textbf{Solve the first equation:}$
$3-2x=5-2x$
Take $2x$ to the left side and $3$ to the right side:
$-2x+2x=5-3$
$0\ne2$ False
This equation has no solution.
$\textbf{Solve the second equation:}$
$3-2x=-(5-2x)$
$3-2x=-5+2x$
Take $2x$ to the left side and $3$ to the right side:
$-2x-2x=-5-3$
$-4x=-8$
Solve for $x$:
$x=\dfrac{-8}{-4}$
$x=2$
The solution is $x=2$