# How do you graph 7/3x <7?

Jan 14, 2018

See a solution process below:

#### Explanation:

Multiply each side of the inequality by $\frac{\textcolor{red}{3}}{\textcolor{b l u e}{7}}$ to solve for $x$ while keeping the inequality balanced:

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{7}} \times \frac{7}{3} x < \frac{\textcolor{red}{3}}{\textcolor{b l u e}{7}} \times 7$

$\frac{\cancel{\textcolor{red}{3}}}{\cancel{\textcolor{b l u e}{7}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{7}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x < \frac{\textcolor{red}{3}}{\cancel{\textcolor{b l u e}{7}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{7}}}$

$x < 3$

To graph this we will draw a vertical line at $3$ 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 left side of the line because the inequality operator contains a "less than" clause:

graph{x < 3 [-10, 10, -5, 5]}