How to solve |x-1| >|2x-1|?

|x-1|>|2x-1|
When x>1
(x-1)>(2x-1) and x>1
x<0 and x>1
When x=1
0>1
When 1/2<x<1
-(x-1)>(2x-1) and 1/2<x<1
x<2/3 and 1/2<x<1
1/2<x<2/3
When x=1/2
1/2>0
x=1/2
When x<1/2
-(x-1)>-(2x-1) and x<1/2
x>0 and x<1/2
0<x<1/2

1/2<x<2/3,x=1/2 or 0<x<1/2
0<x<2/3

Squaring both sides also works since absolute values cannot be negative, we need not care about the direction of the inequality sign.

|x-1|>|2x-1|
(x-1)^2>(2x-1)^2
0>(2x-1+x-1)(2x-1-x+1)
0>(3x-2)x
0< 2/3

2012-05-06 09:58:36 補充：
typo 0<2/3

2012-05-06 09:58:57 補充：
0 < x < 2/3