In which of the given sets of numbers are all the numbers solutions of 4x+7≠23? (1 point)
Responses
1, 2, 3, 4
2, 3, 5, 6
4, 5, 6, 7
3, 4, 6, 7
To solve the inequality 4x+7≠23, we need to isolate x on one side of the equation.
4x+7≠23
4x≠23-7
4x≠16
x≠4
So, x cannot be equal to 4.
Out of the given sets of numbers, only Set 1 contains the number 4, so the set that includes all the solutions of 4x+7≠23 is Set 2: 2, 3, 5, 6.
To determine which set of numbers satisfies the equation 4x + 7 ≠ 23, we can evaluate each set and check if every number in the set makes the inequality true.
Let's start with the first set: 1, 2, 3, 4
For x = 1: 4(1) + 7 = 11 ≠ 23 (True)
For x = 2: 4(2) + 7 = 15 ≠ 23 (True)
For x = 3: 4(3) + 7 = 19 ≠ 23 (True)
For x = 4: 4(4) + 7 = 23 ≠ 23 (False)
Since the last number in the first set (4) does not satisfy the inequality, we can conclude that the entire set does not satisfy 4x + 7 ≠ 23.
Next, let's consider the second set: 2, 3, 5, 6
For x = 2: 4(2) + 7 = 15 ≠ 23 (True)
For x = 3: 4(3) + 7 = 19 ≠ 23 (True)
For x = 5: 4(5) + 7 = 27 ≠ 23 (True)
For x = 6: 4(6) + 7 = 31 ≠ 23 (True)
Every number in the second set satisfies the inequality 4x + 7 ≠ 23. Therefore, the second set (2, 3, 5, 6) is the answer.
We can also quickly check the other two sets to verify our answer:
For the third set (4, 5, 6, 7):
For x = 4: 4(4) + 7 = 23 ≠ 23 (False)
For x = 5: 4(5) + 7 = 27 ≠ 23 (True)
For x = 6: 4(6) + 7 = 31 ≠ 23 (True)
For x = 7: 4(7) + 7 = 35 ≠ 23 (True)
For the fourth set (3, 4, 6, 7):
For x = 3: 4(3) + 7 = 19 ≠ 23 (True)
For x = 4: 4(4) + 7 = 23 ≠ 23 (False)
For x = 6: 4(6) + 7 = 31 ≠ 23 (True)
For x = 7: 4(7) + 7 = 35 ≠ 23 (True)
As we can see, the second set (2, 3, 5, 6) is the only set in which all the numbers satisfy 4x + 7 ≠ 23.