On which of the given sets of numbers are all the numbers solutions of 4x + 7 not equal to 23
2,3,5,6
4,5,6,7
3,4,6,7
1,2,3,4
To determine which set(s) of numbers have all solutions of 4x + 7 not equal to 23, we can substitute each number in each set into the equation and see if any of them satisfy the equation.
1) Set: 2, 3, 5, 6
- Substituting 2: 4(2) + 7 = 8 + 7 = 15 ≠ 23
- Substituting 3: 4(3) + 7 = 12 + 7 = 19 ≠ 23
- Substituting 5: 4(5) + 7 = 20 + 7 = 27 ≠ 23
- Substituting 6: 4(6) + 7 = 24 + 7 = 31 ≠ 23
2) Set: 4, 5, 6, 7
- Substituting 4: 4(4) + 7 = 16 + 7 = 23 ≠ 23 [Not a solution]
- Substituting 5: 4(5) + 7 = 20 + 7 = 27 ≠ 23
- Substituting 6: 4(6) + 7 = 24 + 7 = 31 ≠ 23
- Substituting 7: 4(7) + 7 = 28 + 7 = 35 ≠ 23
3) Set: 3, 4, 6, 7
- Substituting 3: 4(3) + 7 = 12 + 7 = 19 ≠ 23
- Substituting 4: 4(4) + 7 = 16 + 7 = 23 ≠ 23 [Not a solution]
- Substituting 6: 4(6) + 7 = 24 + 7 = 31 ≠ 23
- Substituting 7: 4(7) + 7 = 28 + 7 = 35 ≠ 23
4) Set: 1, 2, 3, 4
- Substituting 1: 4(1) + 7 = 4 + 7 = 11 ≠ 23
- Substituting 2: 4(2) + 7 = 8 + 7 = 15 ≠ 23
- Substituting 3: 4(3) + 7 = 12 + 7 = 19 ≠ 23
- Substituting 4: 4(4) + 7 = 16 + 7 = 23 ≠ 23 [Not a solution]
From the above calculations, it can be observed that on the set: 2, 3, 5, 6, all the numbers are solutions of 4x + 7 not equal to 23.