Question

How do you solve the inequality: `abs(x - 8) < 5`?

Answer 1

`3 < x < 13`

Explanation:

In order to solve this absolute value inequality, you need totake into account the two possible signs the expression inside the modulus can have

• `x-8>0 implies |x-8| = x - 8`

The inequality will become

`x - 8 < 5`

`x < 13`

• `x - 8 < 0 implies |x - 8| = -(x-8)`

This time, the inequality will be

`-(x-8) < 5`

`-x + 8 < 5`

`x > 3`

So, the solution set for this inequality will include any value of `x` that is bigger than `3` and smaller than `13`.

This means that you have `3 < x < 13`, or `x in (3, 13)`.