Question

Which set notation correctly expresses the solution set to the equation 31−9x=4?(1 point)%0D%0AResponses%0D%0A%0D%0A{x=3}%0D%0Aleft brace x equals 3 right brace%0D%0A%0D%0A{3}%0D%0Aleft brace 3 right brace%0D%0A%0D%0A(3)%0D%0Aleft parenthesis 3 right parenthesis%0D%0A%0D%0A%E2%80%8B (x=3)

Answer 1

To solve the equation \( 31 - 9x = 4 \), we first isolate \( x \).

1. Subtract 31 from both sides:
\[
-9x = 4 - 31
\]
\[
-9x = -27
\]

2. Divide both sides by -9:
\[
x = 3
\]

The solution set contains the single value \( x = 3 \).

Using set notation, this can be expressed in different ways:

- As a set with the variable, it can be written as: \(\{ x = 3 \}\)
- As a set with just the value, it can be written as: \(\{ 3 \}\)
- In parentheses, it would be: \( (3) \) but this is not standard set notation.
- The representation \( (x = 3) \) is also not standard set notation for a solution set.

The correct set notation for the solution set is either \(\{ x = 3 \}\) or \(\{ 3 \}\).

Given the options, the correct answer is:

\(\{ 3 \}\)