Question

Which inequality has solutions that include 12 13 and 14

2x < 13 + 15
2x ≤ 12
2x ≥ 34 - 6
2x ≥ 11 + 13
Choose one of the otpions

Answer 1

Let's solve each of the inequalities to find out which one includes the numbers 12, 13, and 14 in its solution set.

1. **Inequality: \( 2x < 13 + 15 \)**
Simplifying gives:
\( 2x < 28 \)
Dividing by 2:
\( x < 14 \)
This includes the solutions 12, 13, and 14 (since it is less than 14).

2. **Inequality: \( 2x ≤ 12 \)**
Dividing by 2 gives:
\( x ≤ 6 \)
This does not include 12, 13, or 14.

3. **Inequality: \( 2x ≥ 34 - 6 \)**
Simplifying gives:
\( 2x ≥ 28 \)
Dividing by 2:
\( x ≥ 14 \)
This includes 14 but not 12 or 13.

4. **Inequality: \( 2x ≥ 11 + 13 \)**
Simplifying gives:
\( 2x ≥ 24 \)
Dividing by 2:
\( x ≥ 12 \)
This includes 12, 13, and 14.

Now, looking at the solutions:

- The first inequality \( x < 14 \) includes 12 and 13 but not 14.
- The second inequality \( x ≤ 6 \) does not include any of 12, 13, or 14.
- The third inequality \( x ≥ 14 \) includes only 14.
- The fourth inequality \( x ≥ 12 \) includes 12, 13, and 14.

Thus, the correct answer is the fourth inequality: **\( 2x ≥ 11 + 13 \)**.