Question

which inequality is represented on the line?
number line from -11 to 11 with open circles at -4 and 1
answer options:
-4 < x < 1
-4 ≤ x ≤ 1
x ≤ -4 or x ≥ 1
x < -4 or x > 1

Explanation:

Step1: Analyze the number line

The number line has open circles at -4 and 1, and the arrows are pointing outward from the interval between -4 and 1. Open circles mean the endpoints are not included, and the direction of the arrows (away from the middle) indicates "or" (disjoint intervals). So we check the options:

• Option 1: \(-4 < x < 1\) is a single interval (between -4 and 1), but the arrows are outward, so no.
• Option 2: \(-4 \leq x \leq 1\) includes endpoints (closed circles) and is a single interval, no.
• Option 3: \(x \leq -4\) or \(x \geq 1\) uses closed circles (since \(\leq\) and \(\geq\)), but the circles on the line are open, so no.
• Option 4: \(x < -4\) or \(x > 1\) has open circles (since \(<\) and \(>\)) and the arrows point outward (x less than -4 or greater than 1), which matches the number line.

Answer:

\(x < -4\) or \(x > 1\)