Question

which graph represents the compound inequality?
-3 < n < 1
options with number lines (omitted image details as per instruction)

Explanation:

Step1: Analyze the inequality

The compound inequality is \(-3 < n < 1\). This means \(n\) is greater than \(-3\) and less than \(1\). On a number line, we use open circles (since the inequalities are strict, not including \(-3\) and \(1\)) and shade the region between \(-3\) and \(1\).

Step2: Evaluate each graph

• First graph: Two separate shaded regions, not between \(-3\) and \(1\). Eliminate.
• Second graph: Shaded from \(-3\) to \(1\) with closed circles, but our inequality is strict (no equal to), so closed circles are wrong. Eliminate.
• Third graph: Two separate shaded regions, not between \(-3\) and \(1\). Eliminate.
• Fourth graph: Open circles at \(-3\) and \(1\), shaded between them, which matches \(-3 < n < 1\).

Answer:

The fourth graph (the one with open circles at -3 and 1, and shading between them)