# How do you solve and graph 7n - 1 < 3n + 5?

May 17, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{1}$ and subtract $\textcolor{b l u e}{3 n}$ from each side of the inequality to isolate the $n$ term while keeping the equation balanced:

$7 n - \textcolor{b l u e}{3 n} - 1 + \textcolor{red}{1} < 3 n - \textcolor{b l u e}{3 n} + 5 + \textcolor{red}{1}$

$\left(7 - \textcolor{b l u e}{3}\right) n - 0 < 0 + 6$

$4 n < 6$

Now, divide each side of the inequality by $\textcolor{red}{4}$ to solve for $n$ while keeping the inequality balanced:

$\frac{4 n}{\textcolor{red}{4}} < \frac{6}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} n}{\cancel{\textcolor{red}{4}}} < \frac{3}{2}$

$n < \frac{3}{2}$

To graph this on a number line we put a hollow circle at $\frac{3}{2}$. The circle is hollow because there is no "or equality to" clause in the inequality operator.

We draw a line from $\frac{3}{2}$ to the left because the inequality operator is a "less than" clause.