Question

solve for c and graph the solution,
-9 ≥ 2c - 17 > -13
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
a segment, ray, or line to delete it.

Explanation:

Step1: Add 17 to all parts

$$\begin{align*} -9 + 17&\geq2c-17 + 17>-13 + 17\\ 8&\geq2c>4 \end{align*}$$

Step2: Divide all parts by 2

$$\begin{align*} \frac{8}{2}&\geq\frac{2c}{2}>\frac{4}{2}\\ 4&\geq c>2 \end{align*}$$

Answer:

The solution is \(2 < c\leq4\). On the number - line, we have an open circle at \(c = 2\) (because \(c>2\)) and a closed circle at \(c = 4\) (because \(c\leq4\)), and we shade the region between them.