# How do you solve and graph 7-n<=19?

Nov 6, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{7}$ from each side of the inequality to isolate the $n$ term while keeping the inequality balanced:

$7 - \textcolor{red}{7} - n \le 19 - \textcolor{red}{7}$

$0 - n \le 12$

$- n \le 12$

Now, multiply each side of the inequality by $\textcolor{b l u e}{- 1}$ to solve for $n$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\textcolor{b l u e}{- 1} \times - n \textcolor{red}{\ge} \textcolor{b l u e}{- 1} \times 12$

$n \textcolor{red}{\ge} - 12$

To graph this we will draw a vertical line at $- 12$ on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x>=-12 [-20, 20, -10, 10]}