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?(1 point)

Question

Responses

{b:b>15}
left brace b colon b greater than 15 right brace

{b:b<3}
left brace b colon b less than 3 right brace

{b:b>3}
left brace b colon b greater than 3 right brace

{b:b<15}

Answer 1

To express the solution set of the inequality \( 3(b−4)+2b>3 \), we first simplify the inequality:

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

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

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

4. Divide by 5: \[ b > 3 \]

The solution set is \( b > 3 \).

The correct set notation that expresses the solutions is:

\({b : b > 3}\)

So the correct response is:

{b:b>3}