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 \( 3x + 4 \geq 16 \).