Given: -2 is greater than

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

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

11+m≤9

Answer 1

To determine which inequality is shown on the number line as having solutions greater than -2, we can analyze each equation.

1. 9 + m ≤ 11

   • Solve for m: \[ m \leq 11 - 9 \ m \leq 2 \]
   • The solution is m (less than or equal to 2), which does not have values greater than -2 only.

2. 11 + m ≥ 9

   • Solve for m: \[ m ≥ 9 - 11 \ m ≥ -2 \]
   • The solution is m (greater than or equal to -2), so it includes values (like m = -2, -1, 0, etc.) that are greater than -2.

3. 9 + m ≥ 11

   • Solve for m: \[ m ≥ 11 - 9 \ m ≥ 2 \]
   • The solution is m (greater than or equal to 2), which also includes values greater than -2.

4. 11 + m ≤ 9

   • Solve for m: \[ m ≤ 9 - 11 \ m ≤ -2 \]
   • The solution is m (less than or equal to -2), which does not include values greater than -2.

From the above analysis, the inequalities that yield solutions greater than -2 are:

• 11 + m ≥ 9: This includes -2 and all values greater than -2 (e.g., -1, 0, etc.).
• 9 + m ≥ 11: This only includes values greater than or equal to 2, and does not necessarily capture everything above -2.

Thus, the answer to your question is

11 + m ≥ 9 (which tells us that m is greater than or equal to -2).