# How do you solve and graph -y+5>=9 or 3y+4< -5?

Dec 22, 2017

See below

#### Explanation:

First rearrange the inequalities so y is the subject:

$- y + 5 \ge 9 \textcolor{w h i t e}{88}$ , $\textcolor{w h i t e}{88} - y \ge 4$ , $\textcolor{w h i t e}{88} y \le - 4$

$3 y + 4 < - 5$ , $\textcolor{w h i t e}{88} 3 y < - 9$ , $\textcolor{w h i t e}{88} y < - 3$

$\textcolor{b l u e}{y \le - 4}$

$\textcolor{b l u e}{y < - 3}$

Graph these two lines as $y = - 4$ and $y = - 3$. Remember to use a dashed line for $y = - 3$, because this is a less than and not a less than or equal to inequality, so the line will not be an included region. We now need to test $y$ values in each region A , B and C. These values have to satisfy both inequalities:

Region A:

$y = - 1$

$- 1 \le - 4 \textcolor{w h i t e}{88}$ False

$- 1 < - 3 \textcolor{w h i t e}{88}$ False

A is not an included region.

Region B:

$y = - 3.5$

$- 3.5 \le - 4 \textcolor{w h i t e}{88}$False

$- 3.5 < - 3 \textcolor{w h i t e}{8}$ True

Region B is not the included region.

Region C:

$y = - 5$

$- 5 \le - 4 \textcolor{w h i t e}{88}$True

$- 5 < - 3 \textcolor{w h i t e}{88}$True

Region C satisfies both, so region C is the included region. 