Which set of terms best represents the graphed solution for the inequality |x|+5≥9

Question

?

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 #

Answer 1

To solve the inequality \(|x| + 5 \geq 9\), we first isolate the absolute value:

\[ |x| \geq 4 \]

This inequality can be split into two cases:

1. \(x \geq 4\)
2. \(x \leq -4\)

Now, let's analyze the options:

• The solutions are \(x \geq 4\) and \(x \leq -4\), which means we have two separate solution sets: one extending to the right from 4 and one extending to the left from -4.
• Since the inequality includes \(\geq\), we use closed circles at the points -4 and 4 because those values satisfy the inequality.

Based on this analysis, the correct option is:

Option #3: closed circles on the end values; two separate solution sets.