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.

Question

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

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

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

11+m≤9

Answer 1

The closed circle at negative 2 and the leftward arrow indicate that the solution includes all values less than or equal to -2.

This means the corresponding inequality is:

\[ m \leq -2 \]

Now, let's analyze the given options to see which one represents this:

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

   Subtracting 9 from both sides gives \( m \leq 2 \) (not correct).

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

   Subtracting 11 from both sides gives \( m \geq -2 \) (not correct).

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

   Subtracting 9 from both sides gives \( m \geq 2 \) (not correct).

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

   Subtracting 11 from both sides gives \( m \leq -2 \) (correct).

Thus, the inequality represented by the number line is:

11 + m ≤ 9