# How do you solve the inequality:  0 < 2y + 8 < 12?

Aug 8, 2015

$- 4 < y < 2$

#### Explanation:

Things you can do to both sides of an inequality while maintaining the validity of the inequality:

• Add or subtract any amount to/from both sides
• Multiply or divide by any amount greater than zero

While it is possible to solve a compound expression (with more than one inequality symbol) it is probably safer to handle the two pieces separately and then recombine.

$0 < 2 y + 8 < 12$
will be treated as
Part 1: $0 < 2 y + 8$ and
Part 2: $2 y + 8 < 12$

Part 1
$0 < 2 y + 8$
$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$- 8 < 2 y$
$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$- 4 < y$

Part 2
$2 y + 8 < 12$
$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$2 y < 4$
$\rightarrow$$\textcolor{w h i t e}{\text{XXXX}}$$y < 2$

Recombining
$\textcolor{w h i t e}{\text{XXXX}}$$- 4 < y < 2$