Question

The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?

Answer 1

Given:

The inequality is:

`|2x-1|>3`

To find:

The solution set for the given inequality.

Solution:

We know that, if
`|x|>a`, then
`x<-a` and
`x>a`.

We have,

`|2x-1|>3`

It can be written as:

`2x-1<-3` or
`2x-1>3`

Case I:

`2x-1<-3`

`2x<-3+1`

`2x<-2`

`x<(-2)/(2)`

`x<-1`

Case II:

`2x-1>3`

`2x>3+1`

`2x>4`

`x>(4)/(2)`

`x>2`

The required solution for the given inequality is
`x<-1` or
`x>2`. The solution set in the interval notation is
`(-\infty,-1)\cup (2,\infty)`.

Therefore, the required solution set is
`(-\infty,-1)\cup (2,\infty)`.