What is a double inequality?

A double inequality is an inequality where there are two signs, as opposed to one.

Ex: an inequality could be 3x < 15

A double inequality could be 3x < 15 < x + 20

If you'd want to solve that double inequality, you split it into to expressions:

3x < 15 and x + 20 > 15

Then just solve.

x < 5 and x > -5

-5 < x < 5