Question

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

Explanation:

Step1: Analyze \(n < - 2\)

For \(n < - 2\), on a number - line, we have an open - circle at \(n=-2\) (because \(n\) is not equal to \(-2\)) and the arrow points to the left.

Step2: Analyze \(n\geq4\)

For \(n\geq4\), on a number - line, we have a closed - circle at \(n = 4\) (because \(n\) can be equal to \(4\)) and the arrow points 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 is all values less than \(-2\) and the other is all values greater than or equal to \(4\).

Answer:

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