Question

In which of the given sets of numbers are all the numbers solutions of 4x+7≠23 ?
4, 5, 6, 7
3, 4, 6, 7
2, 3, 5, 6
1, 2, 3, 4

Answer 1

The numbers that are solutions of 4x + 7 ≠ 23 are those that satisfy the inequality.

Let's evaluate each set of numbers:

1. For the set {4, 5, 6, 7}:
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)
- For x = 5: 4(5) + 7 = 20 + 7 = 27 (Solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)
- For x = 7: 4(7) + 7 = 28 + 7 = 35 (Solution)

2. For the set {3, 4, 6, 7}:
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Not a solution)
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)
- For x = 7: 4(7) + 7 = 28 + 7 = 35 (Solution)

3. For the set {2, 3, 5, 6}:
- For x = 2: 4(2) + 7 = 8 + 7 = 15 (Solution)
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Not a solution)
- For x = 5: 4(5) + 7 = 20 + 7 = 27 (Solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)

4. For the set {1, 2, 3, 4}:
- For x = 1: 4(1) + 7 = 4 + 7 = 11 (Solution)
- For x = 2: 4(2) + 7 = 8 + 7 = 15 (Solution)
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Not a solution)
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)

Therefore, the set in which all the numbers are solutions of 4x + 7 ≠ 23 is {2, 3, 5, 6}.

Answer 2

is that right?

Answer 3

I apologize for the mistake in my previous response. Let's reevaluate the sets of numbers:

1. For the set {4, 5, 6, 7}:
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)
- For x = 5: 4(5) + 7 = 20 + 7 = 27 (Solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)
- For x = 7: 4(7) + 7 = 28 + 7 = 35 (Solution)

2. For the set {3, 4, 6, 7}:
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Solution)
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)
- For x = 7: 4(7) + 7 = 28 + 7 = 35 (Solution)

3. For the set {2, 3, 5, 6}:
- For x = 2: 4(2) + 7 = 8 + 7 = 15 (Solution)
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Solution)
- For x = 5: 4(5) + 7 = 20 + 7 = 27 (Solution)
- For x = 6: 4(6) + 7 = 24 + 7 = 31 (Solution)

4. For the set {1, 2, 3, 4}:
- For x = 1: 4(1) + 7 = 4 + 7 = 11 (Solution)
- For x = 2: 4(2) + 7 = 8 + 7 = 15 (Solution)
- For x = 3: 4(3) + 7 = 12 + 7 = 19 (Solution)
- For x = 4: 4(4) + 7 = 16 + 7 = 23 (Not a solution)

Therefore, the set in which all the numbers are solutions of 4x + 7 ≠ 23 is {2, 3, 5, 6}. Thank you for pointing that out.