Question

which of the following number line graphs is that of the solution set to the inequality $-2x + 12 geq 20$?

Explanation:

Step1: Solve the inequality

$$\begin{align*} -2x + 12&\geq20\\ -2x&\geq20 - 12\\ -2x&\geq8\\ x&\leq\frac{8}{-2}\\ x&\leq - 4 \end{align*}$$

The solution \(x\leq - 4\) means that on the number - line, we have a closed circle at \(-4\) (because the inequality includes equality, i.e., \(x=-4\) is part of the solution) and the line extends to the left (towards more negative values).

Answer:

The first option (the number - line with a closed circle at \(-4\) and the line extending to the left) is the correct graph of the solution set.