# How do you solve and graph the compound inequality  -4<4f+24<4 ?

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
$- 4 < 4 f + 24 < 4$
can be simplified as
$- 1 < f + 6 < 1$
or
$- 7 < f < - 5$

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