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?
{b:b<15}
{b:b<3}
{b:b>15}
{b:b>3}
{b:b>3}
The correct set notation that expresses the solutions is {b: b > 3}.
The solution set of the inequality can be found by solving the inequality and expressing the set of values that satisfy the inequality.
First, let's simplify the inequality:
3(b - 4) + 2b > 3
Distribute the 3 on the left side:
3b - 12 + 2b > 3
Combine like terms:
5b - 12 > 3
Add 12 to both sides to isolate the variable:
5b > 15
Divide both sides by 5 to solve for b:
b > 3
The inequality states that b is greater than 3. Therefore, the correct set notation to express the solutions is {b: b > 3}.
Therefore, the correct answer is {b: b > 3}.