Question

please solve this questions

*WITH STEPS*​

Answer 1

|2x-3|<1

i e 2x-3 lies between -1 and 1

-1<2x-3<1

add 3 on all the sides

2<2x<4

divide by 2 on all sides

1<x<2

|x-1|>=0

I e x-1 lies on real line

so x also lies on real line

|2x-1|/|x-1|>2

case 1: x<1/2 or x>1

2x-1>2x-2

1<2

this happens for every x <1/2 & >1

case 2: 1/2<x<1

2x-1>-2x+2

x>3/4

therefore required answer is 3/4<x<1

hope this helps you out