Question

How do you solve `abs(2x-3)<2`?

Answer 1

Interpreting the modulus, this means

`-2 < 2x - 3 < 2`

Add `3` to all parts to get:

`1 < 2x < 5`

Divide all parts by `2` to get:

`1/2 < x < 5/2`

In general you can do the following to an inequality and maintain its truth (or falsity):

(1) Add or subtract the same value on both sides.
(2) Multiply or divide both sides by the same positive value.
(3) Multiply or divide both sides by the same negative value and reverse the inequality (`<` becomes `>`, `>=` becomes `<=`, etc.).