Question

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 \( 3(b - 4) + 2b > 3 \), let's first simplify it step by step:

1. Distribute \( 3 \) in the term \( 3(b - 4) \):
\[
3b - 12 + 2b > 3
\]

2. Combine like terms:
\[
(3b + 2b) - 12 > 3
\]
\[
5b - 12 > 3
\]

3. Add \( 12 \) to both sides:
\[
5b > 15
\]

4. Divide both sides by \( 5 \):
\[
b > 3
\]

The solution set of the inequality is \( b > 3 \).

In set notation, this is expressed as:
\[
(3, \infty)
\]

So, the correct set notation for the solution is \( (3, \infty) \).