Question

What is the solution set for `abs(3x – 2) < 7`?

Answer 1

`x in (-5/3, 3)`

Explanation:

Since you're dealing with the absolute value of a variable expression, you must take into account the fact that this expression can be negative or positive.

• `3x-2>0 implies |3x-2| = 3x-2`

The inequality becomes

`3x-2 < 7`

`3x < 9 implies x < 3`

• `(3x-2)<0 implies |3x-2| = -(3x-2)`

This time, you get that

`-(3x-2) < 7`

`-3x + 2 < 7`

`-3x < 5 implies x > -5/3`

This means that your original inequality will be true for any value of `x` that is smaller than `3` and bigger than `-5/3`.

The solution interval will thus be `(-5/3, 3)`.