1 answer
(click or scroll down)
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:
\[
\{ b : b > 3 \}
\]