Solve the inequality |x + 1| - |x + 3|≤ 6

Dear Cathy

Case 1:

x+1>0 and x+3>0

==>x>-1

|x + 1| - |x + 3|=-2≤ 6

so for all valueof x greater than -1 will be the solution

Case 2:

x+1>0 and x+3<0

No common solution

case 3:

x+1<0 and x+3<0

==>x<-3

|x + 1| - |x + 3|=-(x + 1) - (-)(x + 3)=2<6

hence for x<-3 inequation holds

hence sol..

x<-3 or x>-1

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IIT Delhi