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To solve the inequality \(3(b-4)+2b>3\), we first simplify the left-hand side.
1. Distribute the 3:
\[
3(b - 4) = 3b - 12
\]
2. Substitute this into the inequality:
\[
3b - 12 + 2b > 3
\]
3. Combine like terms:
\[
(3b + 2b) - 12 > 3 \quad \Rightarrow \quad 5b - 12 > 3
\]
4. Now, add 12 to both sides:
\[
5b > 3 + 12 \quad \Rightarrow \quad 5b > 15
\]
5. Finally, divide both sides by 5:
\[
b > 3
\]
Now, the solution set is all values of \(b\) that are greater than 3. In set notation, this is expressed as:
\[
(3, \infty)
\]
Therefore, the correct set notation expressing the solutions is:
\[
\boxed{(3, \infty)}
\]