To express the solution set of the inequality you provided, let's first clarify the inequality correctly. From what you wrote, it seems there's a slight confusion in the expression.
If we interpret your expression correctly, we can start with the equation given as:
\[ 3(x - 4) + 2b > 3 \]
To isolate \( b \), we rearrange the inequality:
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Distribute the 3: \[ 3x - 12 + 2b > 3 \]
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Move the constant term to the right: \[ 2b > 3 - 3x + 12 \]
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Combine like terms: \[ 2b > -3x + 15 \]
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Divide by 2: \[ b > \frac{-3x + 15}{2} \]
Now, if you want to state that this implies that \( b \) can take values greater than a particular number (let's say 3, for simplicity), then the inequality can be simplified as:
If \( b > 3 \), we want the final solution set in interval notation. Since the problem states that \( b \) should be greater than some value (3), we can express it in set notation as:
\[ b \in (3, \infty) \]
This means that \( b \) is any number greater than 3.
So the correct set notation for the solution set would be:
\[ { b \in \mathbb{R} \mid b > 3 } \]
Or in interval notation:
\[ (3, \infty) \]