Question

now, plot the inequality $-2(3x - 5)>34$ on the number line below. make sure to use the correct type of endpoint.

Explanation:

Step1: Solve the inequality

$$\begin{align*} -2(3x - 5)&>34\\ -6x+10&>34\\ -6x&>34 - 10\\ -6x&>24\\ x&<-4 \end{align*}$$

Step2: Determine the endpoint type

Since the inequality is \(x < - 4\), the endpoint \(x=-4\) is not included. So, it is an open - circle.

Step3: Plot on the number line

On the number line, we make an open - circle at \(-4\) and shade the part of the number line to the left of \(-4\) (towards the negative infinity).

Answer:

Open - circle at \(-4\) and shade the line to the left of \(-4\).