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

First, we need to solve the inequality \( 5 \geq 2n + 11 \).

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

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

This means the solution to the inequality includes all numbers less than or equal to -3.

Now, looking at the graph options:

- A. A closed circle at -3 and a solid line heading right (indicates \( n \geq -3 \)) — **not correct**.

- B. A closed circle at -3 and a solid line heading left (indicates \( n \leq -3 \)) — **correct**.

- C. An open circle at -3 and a solid line heading left (indicates \( n < -3 \)) — **not correct**.

- D. An open circle at -3 and a solid line heading right (indicates \( n > -3 \)) — **not correct**.

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