Question

solve the inequality and graph the solution.
8 + 3c < 2
plot the endpoints. select an endpoint to change it middle of the segment, ray, or line to delete it.

Explanation:

Step1: Subtract 8 from both sides

$$8 + 3c-8<2 - 8$$
$$3c<-6$$

Step2: Divide both sides by 3

$$\frac{3c}{3}<\frac{-6}{3}$$
$$c < - 2$$

To graph the solution:

• The inequality is \(c < - 2\). The endpoint is \(c=-2\). Since the inequality is strict (\(<\)), we use an open circle at \(c = - 2\).
• The solution set includes all real numbers less than \(-2\), so we draw a ray to the left of \(-2\) on the number line.

Answer:

The solution of the inequality \(8 + 3c<2\) is \(c < - 2\). On the number - line, we have an open circle at \(-2\) and a ray extending to the left.