1 answer
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To solve the inequality \( 3(b - 4) + 2b > 3 \), let's first simplify 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. Finally, divide by 5:
\[
b > 3
\]
Now, to express the solution in set notation, it can be represented as:
\[
\{ b \in \mathbb{R} \mid b > 3 \}
\]
or in interval notation as:
\[
(3, \infty)
\]
Both notations correctly express the solution set of the inequality \( b > 3 \).