# How do you solve and graph -5<=-n-6<=0?

May 7, 2017

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{6}$ to each segment of the system of inequalities to isolate the $n$ term while keeping the system balanced:

$- 5 + \textcolor{red}{6} \le - n - 6 + \textcolor{red}{6} \le 0 + \textcolor{red}{6}$

$1 \le - n - 0 \le 6$

$1 \le - n \le 6$

Now, multiply each segment by $\textcolor{b l u e}{- 1}$ to solve for $n$ while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we need to reverse the inequality operators:

$\textcolor{b l u e}{- 1} \cdot 1 \textcolor{red}{\ge} \textcolor{b l u e}{- 1} \cdot - n \textcolor{red}{\ge} \textcolor{b l u e}{- 1} \cdot 6$

$- 1 \textcolor{red}{\ge} n \textcolor{red}{\ge} - 6$

Or

$n \le - 1$; $n \ge - 6$

Or, in interval notation:

$\left[- 6 , - 1\right]$