Question

which set notation correctly expresses the solution set to the equation $31 - 9x = 4$? (1 point)
$\bigcirc\\ (x = 3)$
$\bigcirc\\ (3)$
$\bigcirc\\ \\{x = 3\\}$
$\bigcirc\\ \\{3\\}$

Explanation:

Step1: Solve the equation \(31 - 9x = 4\)

Subtract 31 from both sides: \(-9x = 4 - 31\)
Simplify the right side: \(-9x = -27\)
Divide both sides by -9: \(x = \frac{-27}{-9} = 3\)

Step2: Determine the correct set notation

A solution set in set notation lists the elements (solutions) of the set. For a single solution \(x = 3\), the set notation is \(\{3\}\) (using curly braces for a set, and just the value since it's the solution, not the equation \(x = 3\) inside the set). Parentheses are not used for set notation in this context (they can be for ordered pairs or other uses, but not standard set notation for a single element solution set). So the correct set notation is \(\{3\}\).

Answer:

\(\{3\}\) (corresponding to the option: \(\{3\}\))