Question

The numbers 5, 6, and 7 are solutions of which of the following inequalities? (1 point)(1 point) Responses 3x − 4 > 11 3x − 4 > 11 x + 10 ≠ 15 x + 10 ≠ 15 15 − x < 10 15 − x < 10 3x + 4 ≥ 16

Answer 1

To determine which inequalities have the numbers 5, 6, and 7 as solutions, we will test each inequality one by one.

1. **Inequality:** \( 3x - 4 > 11 \)

- For x = 5:
\( 3(5) - 4 > 11 \)
\( 15 - 4 > 11 \)
\( 11 > 11 \) (False)

- For x = 6:
\( 3(6) - 4 > 11 \)
\( 18 - 4 > 11 \)
\( 14 > 11 \) (True)

- For x = 7:
\( 3(7) - 4 > 11 \)
\( 21 - 4 > 11 \)
\( 17 > 11 \) (True)

Thus, only x = 6 and x = 7 satisfy this inequality.

2. **Inequality:** \( x + 10 \neq 15 \)

- For x = 5:
\( 5 + 10 \neq 15 \)
\( 15 \neq 15 \) (False)

- For x = 6:
\( 6 + 10 \neq 15 \)
\( 16 \neq 15 \) (True)

- For x = 7:
\( 7 + 10 \neq 15 \)
\( 17 \neq 15 \) (True)

Thus, x = 6 and x = 7 satisfy this inequality, but not x = 5.

3. **Inequality:** \( 15 - x < 10 \)

- For x = 5:
\( 15 - 5 < 10 \)
\( 10 < 10 \) (False)

- For x = 6:
\( 15 - 6 < 10 \)
\( 9 < 10 \) (True)

- For x = 7:
\( 15 - 7 < 10 \)
\( 8 < 10 \) (True)

Thus, x = 6 and x = 7 satisfy this inequality, but not x = 5.

4. **Inequality:** \( 3x + 4 \geq 16 \)

- For x = 5:
\( 3(5) + 4 \geq 16 \)
\( 15 + 4 \geq 16 \)
\( 19 \geq 16 \) (True)

- For x = 6:
\( 3(6) + 4 \geq 16 \)
\( 18 + 4 \geq 16 \)
\( 22 \geq 16 \) (True)

- For x = 7:
\( 3(7) + 4 \geq 16 \)
\( 21 + 4 \geq 16 \)
\( 25 \geq 16 \) (True)

Thus, all values of x = 5, x = 6, and x = 7 satisfy this inequality.

**Conclusion:**
The inequality that has x = 5, x = 6, and x = 7 as solutions is **\( 3x + 4 \geq 16 \)**.