Question

select the graph that shows the solution set of $2 \leq n$.
a)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

b)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

c)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

d)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Explanation:

Step1: Analyze the inequality

The inequality is \(2 \leq n\) (which is the same as \(n \geq 2\)). This means we need to represent all numbers greater than or equal to 2 on the number line.

Step2: Determine the correct graph features

• A closed circle (filled dot) is used for "greater than or equal to" or "less than or equal to" because the endpoint (2 in this case) is included in the solution set.
• The arrow should point to the right (towards positive infinity) because we want numbers greater than or equal to 2.

Now let's analyze each option:

• Option A: Has a closed circle at 2 and the arrow points to the right (towards numbers greater than 2). This matches \(n \geq 2\).
• Option B: The arrow points to the left (towards numbers less than 2), which would represent \(n \leq 2\), not \(n \geq 2\).
• Option C: Has an open circle at 2, which is used for strict inequalities (like \(n > 2\) or \(n < 2\)), but our inequality includes 2, so we need a closed circle.
• Option D: Has an open circle at 2 and the arrow points to the left, which is incorrect for \(n \geq 2\).

Answer:

A. The graph with a closed circle at 2 and an arrow pointing to the right (the first graph, labeled A)