Answer
x=$\frac{3}{2}$.
Work Step by Step
Solve the equation: |x-5|=|x+2|
x-5=x+2 or x-5=-(x+2)
x-5-x=x+2-x
-5=2 False.
No solution.
x-5=-(x+2)
x-5=-x-2
x-5+x=-x-2+x
2x-5=-2
2x-5+5=-2+5
$\frac{2x}{2}$=$\frac{3}{2}$
x=$\frac{3}{2}$
x=$\frac{3}{2}$
