# How do you solve and graph the compound inequalities 30 < 10u < 120?

May 5, 2015

Remember you can perform the following operations on both sides of an inequality without changing the inequality:

• Add or subtract any number
• Multiply or divide by any positive (and non-zero) number

So
$30 < 10 u < 120$
can be simplified as
$3 < u < 12$

The image below shows this relation graphed on a number line and in Cartesian space