In which of the given sets of numbers are all the numbers solutions of 18+2x≥36 ?(1 point) Responses 9, 8, 7, 6 9, 8, 7, 6 8, 7, 6 8, 7, 6 0, 3, 9, 12 0, 3, 9, 12 9, 10, 11, 12
The given inequality is 18 + 2x ≥ 36.
Let's test each set of numbers to see if they are all solutions:
1) for 9, 8, 7, 6:
- For x = 9: 18 + 2(9) = 18 + 18 = 36 (satisfies the inequality)
- For x = 8: 18 + 2(8) = 18 + 16 = 34 (does not satisfy the inequality)
- For x = 7: 18 + 2(7) = 18 + 14 = 32 (does not satisfy the inequality)
- For x = 6: 18 + 2(6) = 18 + 12 = 30 (does not satisfy the inequality)
Therefore, not all numbers in this set are solutions.
2) for 0, 3, 9, 12:
- For x = 0: 18 + 2(0) = 18 + 0 = 18 (does not satisfy the inequality)
- For x = 3: 18 + 2(3) = 18 + 6 = 24 (does not satisfy the inequality)
- For x = 9: 18 + 2(9) = 18 + 18 = 36 (satisfies the inequality)
- For x = 12: 18 + 2(12) = 18 + 24 = 42 (satisfies the inequality)
Therefore, not all numbers in this set are solutions.
3) for 9, 10, 11, 12:
- For x = 9: 18 + 2(9) = 36 (satisfies the inequality)
- For x = 10: 18 + 2(10) = 38 (satisfies the inequality)
- For x = 11: 18 + 2(11) = 40 (satisfies the inequality)
- For x = 12: 18 + 2(12) = 42 (satisfies the inequality)
Therefore, all numbers in this set are solutions of the inequality 18 + 2x ≥ 36.
The correct set of numbers where all the numbers are solutions of the inequality is 9, 10, 11, 12.