Question

In which of the given sets of numbers are all the numbers solutions of 4x+7≠23 ?
(1 point)
Responses

3, 4, 6, 7
3, 4, 6, 7

2, 3, 5, 6
2, 3, 5, 6

4, 5, 6, 7
4, 5, 6, 7

1, 2, 3, 4

Answer 1

To determine which set of numbers contains only solutions to the inequality \( 4x + 7 \neq 23 \), we first need to solve the equation \( 4x + 7 = 23 \) to find the value of \( x \) that does not satisfy the inequality.

1. **Solve the equation:**
\[
4x + 7 = 23
\]
Subtract 7 from both sides:
\[
4x = 16
\]
Divide by 4:
\[
x = 4
\]

This means the inequality \( 4x + 7 \neq 23 \) is satisfied for all values except \( x = 4 \).

Now, let's check each set of numbers to see which one does not include \( 4 \):

1. **Set 1: \( 3, 4, 6, 7 \)**
Contains \( 4 \) (not a solution).

2. **Set 2: \( 2, 3, 5, 6 \)**
Does not contain \( 4 \) (all are solutions).

3. **Set 3: \( 4, 5, 6, 7 \)**
Contains \( 4 \) (not a solution).

4. **Set 4: \( 1, 2, 3, 4 \)**
Contains \( 4 \) (not a solution).

**Conclusion:** The only set of numbers where all the numbers are solutions to the inequality \( 4x + 7 \neq 23 \) is **Set 2: \( 2, 3, 5, 6 \)**.