# How do you solve and graph -n+6<7n+4?

Nov 11, 2017

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{n}$ and subtract $\textcolor{b l u e}{4}$ from each side of the inequality to isolate the $n$ term while keeping the inequality balanced:

$\textcolor{red}{n} - n + 6 - \textcolor{b l u e}{4} < \textcolor{red}{n} + 7 n + 4 - \textcolor{b l u e}{4}$

$0 + 2 < \textcolor{red}{1 n} + 7 n + 0$

$2 < \left(\textcolor{red}{1} + 7\right) n$

$2 < 8 n$

Now, divide each side of the inequality by $\textcolor{red}{8}$ to solve for $n$ while keeping the inequality balanced:

$\frac{2}{\textcolor{red}{8}} < \frac{8 n}{\textcolor{red}{8}}$

$\frac{1}{4} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} n}{\cancel{\textcolor{red}{8}}}$

$\frac{1}{4} < n$

We can reverse or "flip" the entire inequality to state the solution in terms of $n$:

$n > \frac{1}{4}$

To graph this we will draw a vertical line at $\frac{1}{4}$ on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain 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> 1/4 [-2, 2, -1, 1]}