Question

which graph represents the compound inequality?
n < -2 or n ≥ 4
options with number lines: first has a closed dot at -2 and open at 4, second has closed at -2 and open at 4 with different arrow directions, third has open at -2 and closed at 4, fourth has open at -2 and closed at 4 with different arrow directions

Explanation:

Step1: Analyze \( n < -2 \)

For \( n < -2 \), the graph should have an open circle at \(-2\) (since \( n \) is not equal to \(-2\)) and an arrow pointing to the left (towards negative infinity).

Step2: Analyze \( n \geq 4 \)

For \( n \geq 4 \), the graph should have a closed circle at \( 4 \) (since \( n \) is equal to \( 4 \)) and an arrow pointing to the right (towards positive infinity).

Step3: Match with options

Now, check each option:

• First option: Closed at \(-2\) (wrong for \( n < -2 \)) and open at \( 4 \) (wrong for \( n \geq 4 \)).
• Second option: Closed at \(-2\) (wrong) and open at \( 4 \), arrow left - right mix (wrong).
• Third option: Open at \(-2\) (correct for \( n < -2 \)) and closed at \( 4 \) (correct for \( n \geq 4 \)), arrows left from \(-2\) and right from \( 4 \) (matches).
• Fourth option: Open at \(-2\) but arrow right from \(-2\) (wrong for \( n < -2 \)) and closed at \( 4 \) (but direction wrong).

Answer:

The third graph (with open circle at -2, closed circle at 4, arrow left from -2, arrow right from 4)