Solve : (|x+1| - x)/x < 1 Share with your friends Share 1 Manbar Singh answered this x+1-xx< 1⇒x+1-xx-1<0⇒x+1-x - xx < 0⇒x+1 - 2xx < 0CASE 1 : When x+1≥0 i.e. x≥-1.In this case : x+1= x + 1So, x+1 - 2xx < 0⇒x+1 - 2xx < 0⇒-x - 1x < 0⇒x - 1x > 0⇒x∈[-1, 0) ∪1, ∞ ........1CASE 2 : When x+1<0 i.e. x < -1In this case x+1 = -x+1So, x+1 - 2xx < 0⇒-x+1 - 2xx < 0⇒-3x - 1x < 0⇒3x+1x > 0⇒x∈-∞, -1 ........2From 1 and 2, we get solution set of the given inequation as,[-1, 0) ∪1, ∞∪-∞, -1 = -∞, 0∪1, ∞ 0 View Full Answer