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

Question

A. (3)
B. {3}
C. {x = 3}
D. (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. Now, divide both sides by -9: \[ x = \frac{-27}{-9} = 3 \]

The solution \(x = 3\) indicates that the only value for \(x\) that satisfies the equation is 3.

Now, we need to determine the appropriate set notation for this solution:

• Option A: \( (3) \) — This does not correctly denote a set; it appears to be an ordered pair representation.
• Option B: \( {3} \) — This correctly represents a set containing the single element 3.
• Option C: \( {x = 3} \) — This represents a set containing a statement rather than just the value of \(x\).
• Option D: \( (x = 3) \) — This also does not correctly represent a set.

The correct choice that represents the solution set is:

B. {3}