please help with this modulus inequality!?

Question

i need to find all real values of x such that | (1/(x+1) -1) | < 2 this is first year of uni question and i'm somewhat stuck :( please help! thanks in advance.

Answer 1

I -x/(x+1) I<2
sign of -x/(x+1) ---------(-1)++++++(0)----------
so for -1 -x/x+1<2 so ( -3x-2)/(x+1) <0 true for x<-1 and x>-2/3
so -2/3
If x<-1 or x > 0
x/(x+1)<2 so(-x-2)/(x+1)<0 so x<-2 and x>-1
so x<-2 and x>0 are solutions
x<-2 and x>-2/3 are the solutions