To simplify the expression \( 9 + 3(4a - 7) - 5a + 6 \), follow these steps:
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Distribute the \( 3 \) into the parentheses: \[ 3(4a - 7) = 12a - 21 \]
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Now substitute this back into the expression: \[ 9 + (12a - 21) - 5a + 6 \]
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Combine like terms. First, combine the constant terms: \[ 9 - 21 + 6 = -6 \]
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Next, combine the \( a \) terms: \[ 12a - 5a = 7a \]
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Now, put it all together: \[ 7a - 6 \]
Thus, the simplified expression is: \[ \boxed{7a - 6} \]
The correct answer is B. \( 7a - 6 \).