Question

which graph represents the compound inequality? n < -2 or n ≥ 4

Explanation:

Step1: Analyze \(n < - 2\)

For \(n < - 2\), we use an open - circle at \(-2\) (since \(n\) cannot equal \(-2\)) and an arrow pointing to the left.

Step2: Analyze \(n\geq4\)

For \(n\geq4\), we use a closed - circle at \(4\) (since \(n\) can equal \(4\)) and an arrow pointing to the right.

Step3: Combine the two inequalities

The compound inequality \(n < - 2\) or \(n\geq4\) has two non - overlapping intervals on the number line.

Answer:

The first option (the one with an open - circle at \(-2\) and arrow to the left and a closed - circle at \(4\) and arrow to the right) represents the compound inequality \(n < - 2\) or \(n\geq4\).