Question

$| frac{2x-1}{x-1} | textgreater 2$

Answer 1

(2x-1)/(x-1)<-2
1)(2x-1+2x-2)/(x-1)<0
(4x-3)/(x-1)<0
x=3/4  x=1
3/4<x<1
2)(2x-1)/(x-1)>2
(2x-1-2x+2)/(x-1)>0
1/(x-1)>0
x-1>0
x>1
Ответ x∈(3/4;1) U (1;∞)