Which set notation correctly expresses the solution set to the equation 31 - 9x = 4?

To solve the equation \( 31 - 9x = 4 \):

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

2. Divide both sides by -9:
\[
x = \frac{-27}{-9}
\]
\[
x = 3
\]

The solution is \( x = 3 \).

To express this in set notation, we can use the notation that describes the solution set. The correct representation would be:

\(\{3\}\) or \(\{x = 3\}\) are set notations for the set containing the solution.

So, the set notation that correctly expresses the solution set to the equation is:

\(\{3\}\) (indicating the set containing the value 3) or \(\{x = 3\}\) (indicating the variable x equals 3).

If asked to choose from the provided options, both \(\{3\}\) and \(\{x = 3\}\) are mathematically valid.