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Which set notation correctly expresses the solution set to the equation

$31-9x=4$ ? (1 point)
$\{ 3\} $
$\{ x=3\} $
$(3)$
$(x=3)$

1 answer

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:

\({ 3 }\)