Question

A number line is shown extending from -10 to 10, a shaded circle is starting at -2 and going beyond -10
The number line is showing the solution of which of the following inequalities
11 + m >= 9
11 + m <= 9
9 + m <= 11
9 + m >= 11

Answer 1

Let's analyze each inequality one by one to determine which one corresponds to the given information about the number line.

1. **11 + m >= 9**
\[
m \geq 9 - 11 \\
m \geq -2
\]
The solution to this inequality is all numbers greater than or equal to -2. On a number line, this would be a shaded region starting at -2 and extending to the right.

2. **11 + m <= 9**
\[
m \leq 9 - 11 \\
m \leq -2
\]
The solution to this inequality is all numbers less than or equal to -2. On a number line, this would be a shaded region starting at -2 and extending to the left.

3. **9 + m <= 11**
\[
m \leq 11 - 9 \\
m \leq 2
\]
The solution to this inequality is all numbers less than or equal to 2. On a number line, this would be a shaded region starting at 2 and extending to the left.

4. **9 + m >= 11**
\[
m \geq 11 - 9 \\
m \geq 2
\]
The solution to this inequality is all numbers greater than or equal to 2. On a number line, this would be a shaded region starting at 2 and extending to the right.

Given that the shaded circle is starting at -2 and extending to the left, this corresponds to the inequality:

**11 + m ≤ 9** (which simplifies to **m ≤ -2**).