Question

which number line shows the solutions to ( n > -2 )?

Explanation:

Step1: Analyze the inequality \( n > -2 \)

The inequality \( n > -2 \) means we are looking for all numbers greater than -2. On a number line, this should be represented with an open circle at -2 (since -2 is not included in the solution, because the inequality is "greater than" not "greater than or equal to") and an arrow pointing to the right (towards positive infinity, or larger numbers).

Step2: Evaluate each number line

• First number line: Open circle at -2, arrow to the right. This matches \( n > -2 \) (open circle for not including -2, right arrow for numbers greater than -2).
• Second number line: Open circle at -2, arrow to the left. This would represent \( n < -2 \), which is incorrect.
• Third number line: Closed circle at -2, arrow to the left. This would represent \( n \leq -2 \), incorrect.
• Fourth number line: Closed circle at -2, arrow to the right. This would represent \( n \geq -2 \), incorrect (we need open circle for \( n > -2 \)).

Answer:

The first number line (with open circle at -2 and arrow to the right)