Question

How do you solve `|-2x+1|<1`?

Answer 1

`x>0andx<1`

Explanation:

`|M+N|<` `KhArr` `M+N<(K)and` `M+N>(-K)`
So,
`|-2x+1|<1hArr-2x+1<1and-2x+1>(-1)`
`hArr-2x<1-1and-2x>(-1)-1`
`hArr-2x<0and-2x>(-2)`
Dividing both sides by (-2),
`hArrxcolor(red)(>)0andxcolor(red)(<)1` (ineqalities change)