The solution set of the inequality 3(b−4)+2b>3 is the set of values of b greater than three. Which set notation correctly expresses the solutions?

To solve the inequality \( 3(b - 4) + 2b > 3 \), let's first simplify it step by step.

1. Distribute the \(3\) in the expression:
\[
3b - 12 + 2b > 3
\]

2. Combine like terms:
\[
5b - 12 > 3
\]

3. Add \(12\) to both sides:
\[
5b > 15
\]

4. Divide both sides by \(5\):
\[
b > 3
\]

Thus, the solution set consists of all values of \(b\) that are greater than \(3\).

In set notation, this can be expressed as:
\[
\{ b \in \mathbb{R} \mid b > 3 \} \quad \text{or} \quad (3, \infty)
\]

Either of these notations correctly represents the solution set.