There are 3 turning points here: −8,−3,4
So we have 4 cases:
1) x<−8
⇒−(x+3)−(4−x)=−(8+x)⇒x=−1
We reject the solution because our condition is not satisfied (−1 is not less than −8)
2)−8≤x<−3
⇒−(x+3)−(4−x)=(8+x)⇒x=−15
We reject the solution because our condition is not satisfied (−15 is not within (−8,−3) interval.)
3)−3≤x<4
⇒(x+3)−(4−x)=(8+x)⇒x=9
We reject the solution because our condition is not satisfied ( 9 is not within (−3,4) interval.)
4) x≥4
⇒(x+3)+(4−x)=(8+x)⇒x=−1
We reject the solution because our condition is not satisfied (−1 is not more than 4 )
Thus there is no solution.