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

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

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

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

11+m≤9
11 plus m less-than-or-equal to 9
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Answer 1

The closed circle at -2 and the leftward arrow indicate that the values for \( m \) are less than or equal to -2.

To determine which inequality corresponds to this, we can analyze the options:

1. \( 9 + m \leq 11 \):

   • Subtracting 9 from both sides gives \( m \leq 2 \). This does not match.

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

   • Subtracting 9 from both sides gives \( m \geq 2 \). This does not match.

3. \( 11 + m \geq 9 \):

   • Subtracting 11 from both sides gives \( m \geq -2 \). This does not match.

4. \( 11 + m \leq 9 \):

   • Subtracting 11 from both sides gives \( m \leq -2 \). This matches the closed circle at -2 and the leftward arrow on the number line.

Therefore, the correct inequality represented by the number line is:

\( 11 + m \leq 9 \).