Find the solution set for...

|2x+9|-|x-6|<=0
Let us consider the following cases:
If x<-9/2
-2x-9+x-6<=0
-x-15<=0
x>=-15
but since x<-9/2,
-15<=x<-9/2
If -9/2<=x<6
2x+9+x-6<=0
3x+3<=0
x<=-1
but since -9/2<=x<6
-9/2<=x<=-1
If x>=6
2x+9-x+6<=0
x+15<=0
x<=-15
but since x>=6
This solution is extraneous.

Thus, combining the first two solutions,
-15<=x<=-1