#### Answer

The solution is $x=1$

#### Work Step by Step

$|4-3x|=|2-3x|$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$4-3x=2-3x$ and $4-3x=-(2-3x)$
$\textbf{Solve the first equation:}$
$4-3x=2-3x$
Take $3x$ to the left side and and $4$ to the right side:
$-3x+3x=2-4$
$0\ne-2$ False
This equation has no solution.
$\textbf{Solve the second equation:}$
$4-3x=-(2-3x)$
$4-3x=-2+3x$
Take $3x$ to the left side and and $4$ to the right side:
$-3x-3x=-2-4$
$-6x=-6$
Solve for $x$:
$x=\dfrac{-6}{-6}$
$x=1$
The solution is $x=1$