Answer
x=4
Work Step by Step
We are given that $|x-3|=|5-x|$
So $x-3=5-x$ or $x-3=-(5-x)$
We can solve both of these equations for x.
For $x-3=5-x$, add 3 to both sides of the equation.
$x=8-x$
Add x to both sides of the equation.
$2x=8$
Divide both sides of the equation by 2.
$x=4$
For $x-3=-(5-x)$, use the distributive property to simplify the right side of the equation.
$x-3=x-5$
Add x to both sides of the equation.
$-3=-5$
This is false, so the only solution is x=4.
