#### Answer

The solutions are $x=2$ and $x=4$

#### Work Step by Step

$|6-2x|+1=3$
Take $1$ to the right side of the equation:
$|6-2x|=3-1$
$|6-2x|=2$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$6-2x=2$ and $6-2x=-2$
$\textbf{Solve the first equation:}$
$6-2x=2$
Take $6$ to the right side:
$-2x=2-6$
$-2x=-4$
Solve for $x$:
$x=\dfrac{-4}{-2}$
$x=2$
$\textbf{Solve the second equation:}$
$6-2x=-2$
Take $6$ to the right side:
$-2x=-2-6$
$-2x=-8$
Solve for $x$:
$x=\dfrac{-8}{-2}$
$x=4$
The solutions are $x=2$ and $x=4$