Question

absolute value inequalities quick check
which set of terms best represents the graphed solution for the inequality $|x| + 5 \geq 9$?
option #1 open circles on the end values, two separate solution sets
option #2 open circles on the end values, a single defined solution set
option #3 closed circles on the end values, two separate solution sets
option #4 closed circles on the end values, a single defined solution set
(1 point)
option #

Explanation:

Step1: Solve the inequality

$$\begin{align*} |x| + 5&\geq9\\ |x|&\geq9 - 5\\ |x|&\geq4 \end{align*}$$

The solution of \(|x|\geq4\) is \(x\leq - 4\) or \(x\geq4\). So there are two separate solution sets.

Step2: Determine the type of circles

Since the inequality is \(\geq\) (not just \(>\)), the end - values (\(x=-4\) and \(x = 4\)) are included in the solution set. Closed circles are used when the value is included in the solution set.

Answer:

Option #3