Question

complete the statements about the ray that represents the solution to $12 - 4x < -20$ on a number line.
select one correct answer in each box to complete each sentence.
the endpoint of the ray should be circle placed at.
the ray should point to the.

Explanation:

Step1: Solve the inequality

$$\begin{align*} 12-4x&<-20\\ 12-4x - 12&<-20 - 12\\ -4x&<-32\\ x&>8 \end{align*}$$

Since the inequality is \(x > 8\), the endpoint is not included.

Step2: Determine the type of circle

For \(x>8\), the endpoint \(x = 8\) is not part of the solution. So, we use an open circle.

Step3: Determine the direction of the ray

Since \(x>8\), values of \(x\) are greater than \(8\). On a number - line, greater values are to the right.

Answer:

The endpoint of the ray should be an open circle placed at \(8\). The ray should point to the right.