Question

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

Explanation:

Step1: Analyze \(n < - 2\)

On a number - line, for \(n < - 2\), we use an open - circle at \(-2\) (because \(-2\) is not included) and draw an arrow to the left.

Step2: Analyze \(n\geq4\)

On a number - line, for \(n\geq4\), we use a closed - circle at \(4\) (because \(4\) is included) and draw an arrow to the right.

Step3: Combine the two inequalities

The compound inequality \(n < - 2\) or \(n\geq4\) means we have two separate intervals on the number - line. One interval is to the left of \(-2\) and the other is to the right of or equal to \(4\).

Answer:

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