Question

what compound inequality describes this graph?
options:
x ≤ 3 or x ≥ 7
x ≤ 3 or x > 7
x < 3 or x ≥ 7
x < 3 or x > 7

Explanation:

Step1: Analyze the left part of the graph

The left part of the number line has a closed circle at 3 and the line is shaded to the left. A closed circle means the endpoint is included, so this part represents \( x \leq 3 \).

Step2: Analyze the right part of the graph

The right part of the number line has an open circle at 7 and the line is shaded to the right. An open circle means the endpoint is not included, so this part represents \( x > 7 \).

Step3: Combine the two parts

The compound inequality is the combination of the two parts with "or", so it is \( x \leq 3 \) or \( x > 7 \).

Answer:

\( x \leq 3 \) or \( x > 7 \) (the option with this inequality)