How to solve!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

| 2x -1 | < x+1 ?

Answer 1

Given expression is | 2x - 1 | < x + 1

                               => 2x - 1 < +/-(x + 1)

                               => 2x - 1 < x + 1 and 2x - 1 > -x - 1

                               => 2x - x < 1 + 1 and 2x + x > -1 + 1

                               => x < 2 and 3x > 0

                               => x < 2 and x > 0

                               => 0 < x < 2

 

Answer 2

The absolute inequality is | 2x - 1 | < x + 1.

Case 1 : 2x-1< 0 ⇒ x < 1/2.

If x < 1/2 then |2x - 1| = -(2x - 1), so we can write the inequality as

- 2x + 1 < x + 1 ⇒ x > 0.

 

Case 2 : 2x-1 ≥ 0 ⇒ x ≥ 1/2.

If x ≥ 1/2 then |2x - 1| = 2x - 1, so we can write the inequality as

2x - 1 < x + 1 ⇒ x < 2.

 

Write the solution of the original inequality as combine the two case

(x<1/2 and x>0) or (x ≥ 1/2 and x<2) ⇒ 0<x<2.