# How do you solve and graph -3<=7c+4<18?

Nov 2, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{4}$ from each segment of the system of inequalities to isolate the $c$ term while keeping the system balanced:

$- 3 - \textcolor{red}{4} \le 7 c + 4 - \textcolor{red}{4} < 18 - \textcolor{red}{4}$

$- 7 \le 7 c + 0 < 14$

$- 7 \le 7 c < 14$

Now, divide each segment by $\textcolor{red}{7}$ to solve for $c$ while keeping the system balanced:

$- \frac{7}{\textcolor{red}{7}} \le \frac{7 c}{\textcolor{red}{7}} < \frac{14}{\textcolor{red}{7}}$

$- 1 \le \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} c}{\cancel{\textcolor{red}{7}}} < 2$

$- 1 \le c < 2$

Or

$c \ge - 1$ and $c < 2$

Or, in interval notation:

$\left[- 1 , 2\right)$

To graph this we will draw vertical lines at $- 1$ and $2$ on the horizontal axis.

The line at $- 1$ will be a solid line because the inequality operator contains an "or equal to" clause. The line at $2$ will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade between the lines to show the interval: 