Question

which compound inequality is represented by the graph?
-5 -4 -3 -2 -1 0 1 2 3 4 5
-3 ≤ x < 1
-3 < x ≤ 1
x ≤ -3 or x > 1
x < -3 or x ≥ 1

Explanation:

Step1: Analyze the graph's endpoints

The graph has a closed circle at -3 (meaning -3 is included, so \( x \geq -3 \) or \( x \leq -3 \)? Wait, no, closed circle at -3: so \( x \) can be -3, so the inequality at -3 is \( x \geq -3 \)? Wait, no, the arrow is to the right from -3? Wait, looking at the number line: the blue line starts at -3 (closed circle, so inclusive) and goes to 1 (open circle, so exclusive). So the values of \( x \) are from -3 (including -3) up to but not including 1. So the compound inequality is \( -3 \leq x < 1 \). Let's check the options:

First option: \( -3 \leq x < 1 \) – matches the closed circle at -3 (inclusive) and open circle at 1 (exclusive), and the line between them.

Second option: \( -3 < x \leq 1 \) – would have open circle at -3 and closed at 1, which doesn't match.

Third option: \( x \leq -3 \) or \( x > 1 \) – would be two separate lines, left of -3 and right of 1, not between.

Fourth option: \( x < -3 \) or \( x \geq 1 \) – also two separate lines, left of -3 (open circle) and right of 1 (closed), not between.

So the correct one is the first option.

Answer:

\( -3 \leq x < 1 \) (the first option: \( -3 \leq x < 1 \))