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?

Question

{b:b > 15}
{b:b < 3}
{b:b > 3}
{b:b < 15}

Answer 1

To solve the inequality \(3(b - 4) + 2b > 3\), first, simplify the left side:

\[ 3b - 12 + 2b > 3 \] \[ 5b - 12 > 3 \]

Next, add 12 to both sides:

\[ 5b > 15 \]

Now, divide by 5:

\[ b > 3 \]

So, the solution set consists of all values of \(b\) that are greater than 3.

In set notation, this can be expressed as:

\[ {b: b > 3} \]

Thus, the correct answer from the provided options is:

\({b: b > 3}\)