In order to determine which set of numbers are all solutions of the equation 4x+7≠23, we need to substitute each number in the given sets into the equation and check if the resulting statement is true or false.
1. Set of numbers: 2, 3, 5, 6
Checking each number in the equation:
For x = 2: 4(2) + 7 ≠ 23 -> 15 ≠ 23 (True)
For x = 3: 4(3) + 7 ≠ 23 -> 19 ≠ 23 (True)
For x = 5: 4(5) + 7 ≠ 23 -> 27 ≠ 23 (False)
For x = 6: 4(6) + 7 ≠ 23 -> 31 ≠ 23 (True)
In this set, 5 does not satisfy the equation, so it is not a solution.
2. Set of numbers: 4, 5, 6, 7
Checking each number in the equation:
For x = 4: 4(4) + 7 ≠ 23 -> 23 ≠ 23 (False)
For x = 5: 4(5) + 7 ≠ 23 -> 27 ≠ 23 (True)
For x = 6: 4(6) + 7 ≠ 23 -> 31 ≠ 23 (True)
For x = 7: 4(7) + 7 ≠ 23 -> 35 ≠ 23 (True)
In this set, 4 does not satisfy the equation, so it is not a solution.
3. Set of numbers: 3, 4, 6, 7
Checking each number in the equation:
For x = 3: 4(3) + 7 ≠ 23 -> 19 ≠ 23 (True)
For x = 4: 4(4) + 7 ≠ 23 -> 23 ≠ 23 (False)
For x = 6: 4(6) + 7 ≠ 23 -> 31 ≠ 23 (True)
For x = 7: 4(7) + 7 ≠ 23 -> 35 ≠ 23 (True)
In this set, 4 does not satisfy the equation, so it is not a solution.
4. Set of numbers: 1, 2, 3, 4
Checking each number in the equation:
For x = 1: 4(1) + 7 ≠ 23 -> 11 ≠ 23 (True)
For x = 2: 4(2) + 7 ≠ 23 -> 15 ≠ 23 (True)
For x = 3: 4(3) + 7 ≠ 23 -> 19 ≠ 23 (True)
For x = 4: 4(4) + 7 ≠ 23 -> 23 ≠ 23 (False)
In this set, 4 does not satisfy the equation, so it is not a solution.
Therefore, the answer is none of the given sets of numbers since there is at least one number in each set that is not a solution of the equation 4x+7≠23.
In which of the given sets of numbers are all the numbers solutions of 4x+7≠23 ?
1. 2, 3, 5, 6
2.4, 5, 6, 7
3.3, 4, 6, 7
4. 1, 2, 3, 4
1 answer