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 simplify it:

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

2. Now, divide both sides by 2 (note that since we are dividing by a positive number, the inequality remains the same):
\[
-3 \geq n
\]
or
\[
n \leq -3
\]

This means that \( n \) can take any value less than or equal to -3.

To represent this on a number line:
- There should be a closed circle at -3, indicating that -3 is included in the solution (since the inequality is "less than or equal to").
- A bold line should extend leftwards from -3, indicating that all values less than -3 are included in the solution.

Among the options given, the correct representation 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.**