Question

what compound inequality describes this graph?
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.

Explanation:

Step1: Analyze the left part of the graph

The left part has a closed dot at 4 and the line goes to the left, so this represents \( x \leq 4 \).

Step2: Analyze the right part of the graph

The right part has an open dot at 7 and the line goes to the right, so this represents \( x > 7 \).

Step3: Combine the two inequalities

Since the two parts are separate (the graph has two distinct segments), we use "or" to combine them. So the compound inequality is \( x \leq 4 \) or \( x > 7 \).

Answer:

\( x \leq 4 \) or \( x > 7 \)