Question

How do you solve `|2x-3|<2`?

Answer 1

The solution is `x in (1/2,5/2)`

Explanation:

The inequality is

`|2x-3|<2`

Therefore,

`2x-3<2` and `2x-3>-2`

The first equation gives

`2x<2+3`

`x<5/2`

The second equation gives

`2x>-2+3`

`x>1/2`

Combining the `2` solutions

`x in (1/2,5/2)`

Answer 2

`1/2 < x <5/2`

Explanation:

`"Inequalities of the type "|x|< a`

`"Always have solutions of the form"`

`-a < x < a`

`rArr-2< 2x-3 < 2`

`"add 3 to all three intervals"`

`-2color(red)(+3)< 2xcancel(-3)cancel(color(red)(+3))<2color(red)(+3)`

`rArr1< 2x <5`

`"divide all three intervals by 2"`

`rArr1/2 < x < 5/2`