The solution set of the inequality \(3(b-4)+2b>3\) is the set of values of b greater than three. Which set notation correctly expresses the solutions?

Answer 1

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:

\[ \boxed{(3, \infty)} \]