Question

{x=3}
left brace x equals 3 riWhich set notation correctly expresses the solution set to the equation 31−9x=4?(1 point)
Responsesght brace

(3)
left parenthesis 3 right parenthesis

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

{3}

Answer 1

To express the solution set of the equation \(3(1 - 9x) = 4\), we first need to solve for \(x\).

1. Start with the equation:
\[
3(1 - 9x) = 4
\]

2. Divide both sides by 3:
\[
1 - 9x = \frac{4}{3}
\]

3. Subtract 1 from both sides:
\[
-9x = \frac{4}{3} - 1
\]

Convert 1 to a fraction:
\[
1 = \frac{3}{3}
\]
Now calculate:
\[
-9x = \frac{4}{3} - \frac{3}{3} = \frac{4 - 3}{3} = \frac{1}{3}
\]

4. Divide both sides by -9:
\[
x = -\frac{1}{27}
\]

The solution set for the equation is \(-\frac{1}{27}\). In set notation, it can be expressed as:

\[
\{-\frac{1}{27}\}
\]

However, since your options are specifically for the solution \(x = 3\), it seems there may have been a misunderstanding in the equation setup or the choices provided.

If we assume the correct solution given as \(x = 3\), in set notation, it would be best represented as:

\(\{3\}\)

So the correct answer among your responses is:

\(\{3\}\)