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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) Responses {b:b>15} left brace b colon b greater than 15 right brace {b:b>3} left brace b colon b greater than 3 right brace {b:b<15} left brace b colon b less than 15 right brace {b:b<3}

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To determine the correct set notation for the solution set of the inequality \(3(b - 4) + 2b > 3\), let's first solve the inequality:

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

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

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

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

Now we see that the solution set is indeed \(b > 3\).

The correct set notation that expresses these solutions is: \[ {b : b > 3} \]

So, the correct response is: \({b : b > 3}\) (left brace b colon b greater than 3 right brace).