# How do you solve and graph −44> −2x − 8 ≥ −8?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

To solve a system of inequalities you need to perform each operation across the entire system to keep the system of inequalities balanced. First, we will add $\textcolor{red}{8}$ to each segment of the inequality:

$- 44 + \textcolor{red}{8} > - 2 x - 8 + \textcolor{red}{8} \ge - 8 + \textcolor{red}{8}$

$- 36 > - 2 x - 0 \ge 0$

$- 36 > - 2 x \ge 0$

Now, we will divide each segment of the system by $\textcolor{b l u e}{- 2}$ to solve for $x$. However, because we are multiplying or dividing by a negative term we must reverse the inequality signs:

$\frac{- 36}{\textcolor{b l u e}{- 2}} \textcolor{red}{<} \frac{- 2 x}{\textcolor{b l u e}{- 2}} \textcolor{red}{\le} \frac{0}{\textcolor{b l u e}{- 2}}$

$18 \textcolor{red}{<} \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 2}}} x}{\cancel{\textcolor{b l u e}{- 2}}} \textcolor{red}{\le} 0$

$18 < x \le 0$