# How do you solve and graph 3/2x-7<2?

Sep 3, 2017

See a solution process below:

#### Explanation:

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

$\frac{3}{2} x - 7 + \textcolor{red}{7} < 2 + \textcolor{red}{7}$

$\frac{3}{2} x - 0 < 9$

$\frac{3}{2} x < 9$

Now, multiply each side of the inequality by $\frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}}$ to solve for $x$ while keeping the inequality balanced:

$\frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}} \times \frac{3}{2} x < \frac{\textcolor{red}{2}}{\textcolor{b l u e}{3}} \times 9$

$\frac{\cancel{\textcolor{red}{2}}}{\cancel{\textcolor{b l u e}{3}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x < \frac{18}{\textcolor{b l u e}{3}}$

$x < 6$

To graph this we will draw a vertical line at $6$ 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<6 [-10, 10, -5, 5]}