Question

what compound inequality describes this graph?
number line with 639, 640, 641 (open circle), 642, 643, 644, 645 (open circle), 646, 647, arrows left from 641 and right from 645
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 of the graph has an open circle at 641 and the line goes to the left, so this represents \( x < 641 \).

Step2: Analyze the right part of the graph

The right part of the graph has an open circle at 645 and the line goes to the right, so this represents \( x > 645 \).

Step3: Combine the two inequalities

Since the graph shows two separate regions (left of 641 and right of 645), we use the "or" connector. So the compound inequality is \( x < 641 \) or \( x > 645 \).

Answer:

\( x < 641 \) or \( x > 645 \)