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 arrow starts from the open circle at 1 and goes to the left, so this represents \( x < 1 \) (open circle means not including 1).

Step2: Analyze the right part of the graph

The right arrow starts from the open circle at 3 and goes to the right, so this represents \( x > 3 \) (open circle means not including 3).

Step3: Combine the two inequalities

Since the graph has two separate parts (left of 1 and right of 3), we use "or" to combine them. So the compound inequality is \( x < 1 \) or \( x > 3 \).

Answer:

\( x < 1 \) or \( x > 3 \)