Question

5
≥
2
n
+
11
Which graph represents the solution to the inequality shown?

A.
The number line shows numbers from -3 to 1. There is a closed circle at -3, a bold line from -3 heading rightwards.

B.
The number line shows numbers from -3 to 1. There is a closed circle at -3, a bold line from -3 heading leftwards.

C.
The number line shows numbers from -3 to 1. There is a open circle at -3, a bold line from -3 heading leftwards.

D.
The number line shows numbers from -3 to 1. There is a open circle at -3, a bold line from -3 heading rightwards.

Answer 1

To solve the inequality \( 5 \geq 2n + 11 \), we first rearrange it:

1. Subtract 11 from both sides:
\[
5 - 11 \geq 2n
\]
\[
-6 \geq 2n
\]

2. Divide both sides by 2:
\[
-3 \geq n
\]
or equivalently,
\[
n \leq -3
\]

The inequality \( n \leq -3 \) indicates that the solution includes all numbers less than or equal to -3.

Now we analyze the given choices:

- A: Closed circle at -3 with a line heading right (incorrect, as it implies numbers greater than or equal to -3).
- B: Closed circle at -3 with a line heading left (correct, implies numbers less than or equal to -3).
- C: Open circle at -3 with a line heading left (incorrect, as an open circle indicates -3 is not included).
- D: Open circle at -3 with a line heading right (incorrect, as it implies numbers greater than -3).

The correct answer is **B**, which represents the inequality \( n \leq -3 \).