# How do you solve and graph -3<2x<=6?

Jan 28, 2018

See a solution process below:

#### Explanation:

Divide each segment of the system of inequalities by $\textcolor{red}{2}$ to solve for $x$ while keeping the system balanced:

$- \frac{3}{\textcolor{red}{2}} < \frac{2 x}{\textcolor{red}{2}} \le \frac{6}{\textcolor{red}{2}}$

$- \frac{3}{2} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c}{2}}} x}{\cancel{\textcolor{red}{2}}} \le 3$

$- \frac{3}{2} < x \le 3$

Or

$x > - \frac{3}{2}$; $x \le 3$

Or, in interval notation:

$\left(- \frac{3}{2} , 3\right]$

To graph this we will draw vertical line at $- \frac{3}{2}$ and $3$ on the horizontal axis.

The line at $- \frac{3}{2}$ will be a dashed line because the inequality operator does not contain an "or equal to" clause. This indicates $- \frac{3}{2}$ is not part of the solution set.

The line at $3$ will be a solid line because the inequality operator contains an "or equal to" clause. This indicates $3$ is part of the solution.

We will shade between the two lines to show the solution set. 