Question

solve the inequality and graph the solution.
6(r + 1) ≤ -6
plot the endpoints. select an endpoint to change it from closed to open. select the
middle of the segment, ray, or line to delete it.

Explanation:

Step1: Solve the inequality

$$\begin{align*} 6(r + 1)&\leq-6\\ r+1&\leq\frac{-6}{6}\\ r + 1&\leq-1\\ r&\leq-1-1\\ r&\leq-2 \end{align*}$$

Step2: Graph the solution

Since \(r\leq - 2\), we plot a closed - circle at \(r=-2\) (because the inequality is \(\leq\)) and draw a ray to the left (towards the smaller numbers) on the number line.

Answer:

The solution of the inequality \(6(r + 1)\leq-6\) is \(r\leq-2\). On the number line, we have a closed - circle at \(-2\) and a ray extending to the left.