Question

solve for k and graph the solution.
1≥k + 5 > -4
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: Subtract 5 from all parts

$$\begin{align*} 1-5&\geq k + 5-5> - 4-5\\ -4&\geq k>-9 \end{align*}$$

Answer:

The solution is $-9 < k\leq - 4$. On the number - line, at $k = - 9$, we have an open circle (because $k>-9$) and at $k=-4$, we have a closed circle (because $k\leq - 4$), and we shade the region between them.