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To solve the inequality \( 3(b - 4) + 2b > 3 \), we start by simplifying it:
1. Distribute the 3:
\[
3b - 12 + 2b > 3
\]
2. Combine like terms:
\[
5b - 12 > 3
\]
3. Add 12 to both sides:
\[
5b > 15
\]
4. Divide by 5:
\[
b > 3
\]
The solution set indicates that \( b \) is greater than 3. In set notation, this can be expressed as:
\[
\{ b \in \mathbb{R} \mid b > 3 \}
\]
Alternatively, it can be represented using interval notation:
\[
(3, \infty)
\]
Both notations are correct representations of the solution set.