solve |x+3|-|5-x|=|x+2|

For convenience we write: |x+3|=|x+2|+|x-5| 

We'll solve by checking the following cases: 
+ + +
+ + -
+ - +
+ - - 



+++
x+3=x+2+x-5
x=6 (yes-solution) 

++-
x+3=x+2-(x-5)
x=4 (yes-solution) 

+-+
x+3=-(x+2)+x-5
x=-10 (no-not a solution) 

+--
x+3=-(x+2)-(x-5)
x=0 (no-not a solution) 

solution {4, 6} 

:)