Question

Solution sets of equations and inequities quick check which set notations correctly expresses the solution set to the equation 31 - 9x = 4

Answer 1

To solve the equation \( 31 - 9x = 4 \), 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 to the equation is \( x = 3 \).

To express the solution set in set notation, it can be written as:
\[
\{3\}
\]
This denotes that the solution set contains the single element \( 3 \).

If you were to express it in interval notation, since it is a single solution, it would be:
\[
[3, 3]
\]

However, the simplest and most common set notation for a single solution is \(\{3\}\).