The solution set of the inequality $3(b-4)+2b\gt 3$ is the set of values of

To solve the inequality \(3(b-4) + 2b > 3\), we start by simplifying the left-hand side:

1. Distribute \(3\):
\[
3(b - 4) = 3b - 12
\]
So the inequality becomes:
\[
3b - 12 + 2b > 3
\]

2. Combine the terms with \(b\):
\[
(3b + 2b) - 12 > 3 \implies 5b - 12 > 3
\]

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

4. Now, divide by \(5\):
\[
b > 3
\]

The solution set is therefore all values of \(b\) greater than \(3\).

In set notation, this is expressed as:
\[
\{ b : b > 3 \}
\]

Thus, the correct choice that represents the solution set is:
\[
\{ b : b > 3 \}
\]