# How do you solve and graph 4<y+2<-3(y-2)+24?

Jul 24, 2015

$2 < y < 7$
$\textcolor{w h i t e}{\text{XXXX}}$(see below for number line graph)

#### Explanation:

Treat the two inequalities separately then recombine.

Inequality 1: $\textcolor{w h i t e}{\text{XXXX}}$$4 < y + 2$
Subtracting $2$ from both sides gives:
$\textcolor{w h i t e}{\text{XXXX}}$$2 < y$

Inequality 2: $\textcolor{w h i t e}{\text{XXXX}}$$y + 2 < - 3 \left(y - 2\right) + 24$
Simplifying the $- 3 \left(y - 2\right)$ term:
$\textcolor{w h i t e}{\text{XXXX}}$$y + 2 < - 3 y + 6 + 24$
Basic arithmetic
$\textcolor{w h i t e}{\text{XXXX}}$$y + 2 < - 3 y + 30$
Add $\left(3 y - 2\right)$ to both sides
$\textcolor{w h i t e}{\text{XXXX}}$$4 y < 28$
Divide both sides by $4$
$\textcolor{w h i t e}{\text{XXXX}}$$y < 7$

Recombining
$\textcolor{w h i t e}{\text{XXXX}}$$2 < y < 7$