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

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

9+m≤11

Answer 1

The closed circle at -2 and a leftward arrow indicates that the solution includes -2 and all numbers less than -2. This can be expressed as:

m ≤ -2

Now we need to deduce which of the listed inequalities corresponds to this:

1. 11 + m ≤ 9 can be manipulated:

   • Subtract 11 from both sides:
   • m ≤ 9 - 11
   • m ≤ -2 ✅ (Match)

2. 9 + m ≥ 11

   • Subtract 9 from both sides:
   • m ≥ 11 - 9
   • m ≥ 2 ❌ (No match)

3. 11 + m ≥ 9

   • Subtract 11 from both sides:
   • m ≥ 9 - 11
   • m ≥ -2 ❌ (No match)

4. 9 + m ≤ 11

   • Subtract 9 from both sides:
   • m ≤ 11 - 9
   • m ≤ 2 ❌ (No match)

Thus, the inequality that matches the solution shown on the number line is:

11 + m ≤ 9.