Question

What is the solution set for `absx < 15`?

Answer 1

`-15 < x < 15`

Explanation:

All you really have to do to solve this absolute value inequality is to take into account the two possible signs `x` can have.

• `x>0 implies |x| = x`

In this case, the inequality becomes

`x < 15`

• `x<0 implies |x| = -x`

This time, you have

`-x < 15 implies x > -15`

So, the solution set to this inequality will include any value of `x` that simultaneously satisfies these conditions, `x > -15` and `x<15`.

Therefore, the solution set will be `-15 < x < 15`, or `x in (-15, 15)`.