Question

Which inequality has solutions that include 12, 13, and 14? Responses 2x<13+15 2x<13+15 - no response given 2x≥34−6 2 x is greater than or equal to 34 minus 6 - no response given 2x≥11+13 2 x is greater than or equal to 11 plus 13 - no response given 2x≤12

Answer 1

To determine which inequality has solutions that include 12, 13, and 14, we'll evaluate each inequality one by one.

1. **For the inequality \(2x < 13 + 15\)**:
- Simplifying this gives \(2x < 28\).
- Dividing by 2: \(x < 14\).
- This includes solutions for \(x = 12\) and \(x = 13\) but does not include \(x = 14\).

2. **For the inequality \(2x \geq 34 - 6\)**:
- Simplifying this gives \(2x \geq 28\).
- Dividing by 2: \(x \geq 14\).
- This includes \(x = 14\) but does not include \(x = 12\) or \(x = 13\).

3. **For the inequality \(2x \geq 11 + 13\)**:
- Simplifying this gives \(2x \geq 24\).
- Dividing by 2: \(x \geq 12\).
- This includes \(x = 12\), \(x = 13\), and \(x = 14\).

4. **For the inequality \(2x \leq 12\)**:
- Simplifying this gives \(x \leq 6\).
- This does not include 12, 13, or 14.

Among the inequalities, the one that includes all three solutions \(12\), \(13\), and \(14\) is:

**\(2x \geq 11 + 13\)**.