[x+4]>0

l x + 4 l  > 0     take the expression out of the absolute value 

We have

x + 4 > 0      subtract 4 from both sides

x > -4

We also have

x + 4 < 0     subtract 4 from both sides

x < -4

So the solution is  (-∞, -4) U (-4, ∞ )