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

Answer 1

To determine which set of numbers contains all the solutions of the inequality \(4x + 7 \neq 23\), we first need to find the value of \(x\) that makes the equation \(4x + 7 = 23\).

Starting with the equation:

\[ 4x + 7 = 23 \]

Subtract 7 from both sides:

\[ 4x = 16 \]

Now, divide both sides by 4:

\[ x = 4 \]

Thus, the inequality \(4x + 7 \neq 23\) means \(x\) can take any value except \(4\).

Now, let's evaluate the provided sets of numbers to find which set excludes 4:

1. Set 1: \(1, 2, 3, 4\) - This set includes 4.
2. Set 2: \(4, 5, 6, 7\) - This set includes 4.
3. Set 3: \(2, 3, 5, 6\) - This set does not include 4.
4. Set 4: \(3, 4, 6, 7\) - This set includes 4.

Only Set 3: \(2, 3, 5, 6\) contains numbers that are all solutions to \(4x + 7 \neq 23\).