Which set notation correctly expresses the solution set to the equation

To solve the equation \(31 - 9x = 4\), we can follow these steps:

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

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

The solution of the equation is \(x = 3\).

Now, to express this solution in set notation, we denote the solution set containing the element \(3\). The correct set notation for the solution set is:

\[
\{ 3 \}
\]

The options given are:

- \(\{ 3\}\)
- \(\{ x=3\}\)
- \((3)\)
- \((x=3)\)

Out of these options, the correct one is \(\{ 3 \}\) since it represents the set containing the solution \(3\).

Therefore, the correct answer is:

\(\{ 3 \}\)