(1−|x|)/(2−|x|)≥0.Find x

Question

(1−|x|)/(2−|x|)≥0.Find x

Answer 1

(1- lxl )/(2 - lxl) ≥ 0

 

There are 2 cases to consider:

 

Case 1:  numerator ≥ 0 and denominator > 0

 

               lxl ≤ 1 and lxl < 2     So, -1≤x≤1 and -2<x<2.  

 

               For the inequalities to be true, we must have -1≤x≤1.

 

Case 2:  numerator < 0 and denominator < 0

 

              lxl>1 and lxl>2   So, x>1 or x<-1, and x>2 or x<-2,

 

              So,  x>2 or x<-2.  

 

Solution set:  (-∞,-2) ∪ [-1,1] ∪ (2,∞)