In which of the given sets of numbers are all the numbers solutions of 18 + 2 x ≥ 36 ?

Answer 1

The given inequality is 18 + 2x ≥ 36.

Testing each set of numbers:

1) {10, 12, 16}:
- 18 + 2(10) = 38, which is greater than 36. Therefore, 10 is not a solution.
- 18 + 2(12) = 42, which is greater than 36. Therefore, 12 is not a solution.
- 18 + 2(16) = 50, which is greater than 36. Therefore, 16 is not a solution.

2) {9, 11, 14, 18}:
- 18 + 2(9) = 36, which is equal to 36. Therefore, 9 is a solution.
- 18 + 2(11) = 40, which is greater than 36. Therefore, 11 is a solution.
- 18 + 2(14) = 46, which is greater than 36. Therefore, 14 is a solution.
- 18 + 2(18) = 54, which is greater than 36. Therefore, 18 is not a solution.

3) {1, 2, 3, 4, 5}:
- 18 + 2(1) = 20, which is less than 36. Therefore, 1 is not a solution.
- 18 + 2(2) = 22, which is less than 36. Therefore, 2 is not a solution.
- 18 + 2(3) = 24, which is less than 36. Therefore, 3 is not a solution.
- 18 + 2(4) = 26, which is less than 36. Therefore, 4 is not a solution.
- 18 + 2(5) = 28, which is less than 36. Therefore, 5 is not a solution.

Therefore, the set of numbers {9, 11, 14} are all solutions to the given inequality 18 + 2x ≥ 36.