Use the image to answer the question.

Question

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed circle is plotted on the number line at negative 2. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

The number line shows the solution of which of the following inequalities?

(1 point)
Responses

11+m≤9
11 plus m less-than-or-equal to 9

9+m≥11
9 plus m is greater than or equal to 11

9+m≤11
9 plus m less-than-or-equal-to 11

11+m≥9

Answer 1

To determine the inequality represented by the number line, we analyze the information given.

The closed circle at -2 indicates that -2 is included in the solution, and the leftward arrow indicates that the solution extends to values less than or equal to -2. Therefore, the solutions represent all values of \( m \) such that \( m \leq -2 \).

Now we'll rewrite the possible inequalities given in the responses:

1. \( 11 + m \leq 9 \)
2. \( 9 + m \geq 11 \)
3. \( 9 + m \leq 11 \)
4. \( 11 + m \geq 9 \)

Let's analyze the first inequality:

1. \( 11 + m \leq 9 \)
   • Subtracting 11 from both sides gives us: \[ m \leq 9 - 11 \] \[ m \leq -2 \]

This matches with what we saw on the number line.

Since the other inequalities can be analyzed in a similar way, let’s quickly examine them to confirm:

2. \( 9 + m \geq 11 \)

   • This simplifies to \( m \geq 2 \) (not matching).

3. \( 9 + m \leq 11 \)

   • This simplifies to \( m \leq 2 \) (not matching).

4. \( 11 + m \geq 9 \)

   • This simplifies to \( m \geq -2 \) (not matching).

Only the first inequality, \( 11 + m \leq 9 \), simplifies to \( m \leq -2 \), which matches the representation on the number line.

Therefore, the solution of the given number line corresponds to the inequality:

11 + m ≤ 9