The numbers 5, 6, and 7 are solutions of which of the following inequalities?
A. 15 - x < 10
B. 3x - 4 > 11
C. 3x + 4 ≥ 16
D. x + 10 ≠ 15
We can substitute each number into each inequality to see which ones are solutions.
A. 15 - 5 = 10, which is not less than 10. 15 - 6 = 9, which is less than 10. 15 - 7 = 8, which is also less than 10. Therefore, 5, 6, and 7 are not solutions of 15 - x < 10.
B. 3(5) - 4 = 11, which is equal to 11. 3(6) - 4 = 14, which is greater than 11. 3(7) - 4 = 17, which is also greater than 11. Therefore, 5 is not a solution, but 6 and 7 are solutions of 3x - 4 > 11.
C. 3(5) + 4 = 19, which is greater than or equal to 16. 3(6) + 4 = 22, which is also greater than or equal to 16. 3(7) + 4 = 25, which is also greater than or equal to 16. Therefore, 5, 6, and 7 are solutions of 3x + 4 ≥ 16.
D. 5 + 10 = 15, which is equal to 15. 6 + 10 = 16, which is not equal to 15. 7 + 10 = 17, which is not equal to 15. Therefore, 5 is a solution, but 6 and 7 are not solutions of x + 10 ≠ 15.
Thus, the answer is C.