the solution set of the inequality 3(x - 4) + 2b 3 is the set of values of b greater than three. which set notation correctly expresses the solutions

To express the solution set of the inequality you provided, let's first clarify the inequality correctly. From what you wrote, it seems there's a slight confusion in the expression.

If we interpret your expression correctly, we can start with the equation given as:

\[ 3(x - 4) + 2b > 3 \]

To isolate \( b \), we rearrange the inequality:

1. Distribute the 3:
\[ 3x - 12 + 2b > 3 \]

2. Move the constant term to the right:
\[ 2b > 3 - 3x + 12 \]

3. Combine like terms:
\[ 2b > -3x + 15 \]

4. Divide by 2:
\[ b > \frac{-3x + 15}{2} \]

Now, if you want to state that this implies that \( b \) can take values greater than a particular number (let's say 3, for simplicity), then the inequality can be simplified as:

If \( b > 3 \), we want the final solution set in interval notation. Since the problem states that \( b \) should be greater than some value (3), we can express it in set notation as:

\[ b \in (3, \infty) \]

This means that \( b \) is any number greater than 3.

So the correct set notation for the solution set would be:

\[
\{ b \in \mathbb{R} \mid b > 3 \}
\]

Or in interval notation:

\[
(3, \infty)
\]