Question 13758
|x+4|= x + 4 ; where {{{x>=-4}}}
|x+4|= -(x + 4); where {{{x<-4}}}

5-|x+4|<-3

case (i): 
5-(x+4)<-3; where {{{x>=-4}}}
5-(x+4)<-3
5-x-4<-3
-x-4+5<-3
-x+1<-3
-x<-3-1
-x<-4
x>4
Solution for this case is x>4

case (ii):
5-(-(x+4))<-3; where {{{x>=-4}}}
5+(x+4)<-3
5+x+4<-3
x+9<-3
x<-3-9
x<-12
There is no solution for this case.

So, solution for this inequality is x>4.
OK