Question

Which set notation correctly expresses the solution set to the equation 31−9x=4 ?(1 point)
Responses..

{3}
left brace 3 right brace

​ (x=3)
​ left parenthesis x equals 3 right parenthesis

(3)
left parenthesis 3 right parenthesis

{x=3}

Answer 1

To express the solution set to the equation \( 31 - 9x = 4 \), we first solve for \( x \):

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

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

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

Now, let's look at the responses provided for the correct set notation:

- \{3\} (this denotes the set containing the number 3)
- (x=3) (this is an equation, not set notation)
- (3) (this denotes the number 3, not as a set)
- \{x=3\} (this denotes a set containing the equation but is not typically how solutions are expressed)

The correct response for the solution set is **\{3\}**, which denotes the set containing the solution.