Question

solve the inequality and graph the solution.
7 < -17 + 3r
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Isolate the term with the variable

Add \(17\) to both sides of the inequality \(7 < - 17+3r\).
$$7 + 17< - 17+17 + 3r$$
$$24<3r$$

Step2: Solve for \(r\)

Divide both sides of the inequality \(24 < 3r\) by \(3\).
$$\frac{24}{3}<\frac{3r}{3}$$
$$8 < r$$
Which can be written as \(r>8\)

To graph \(r > 8\):

• The endpoint is at \(r = 8\). Since the inequality is \(>\) (not \(\geq\)), the endpoint is open.
• The ray extends to the right (towards larger values of \(r\))

Answer:

The solution of the inequality is \(r>8\). On the number - line, there is an open circle at \(8\) and a ray extending to the right.