To simplify the expression \( 2(3v + 9) - 14 - 6(-5v - 4) \), we will follow the order of operations: distribute, combine like terms, and simplify.
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Distribute \( 2 \) in \( 2(3v + 9) \): \[ 2(3v) + 2(9) = 6v + 18 \]
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Distribute \( -6 \) in \( -6(-5v - 4) \): \[ -6(-5v) - 6(-4) = 30v + 24 \]
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Now substitute these back into the expression: \[ 6v + 18 - 14 + 30v + 24 \]
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Combine like terms:
- Combine the \( v \) terms: \[ 6v + 30v = 36v \]
- Combine the constant terms: \[ 18 - 14 + 24 = 28 \]
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So the simplified expression is: \[ 36v + 28 \]
Thus, the answer is \( \boxed{A} : 36v + 28 \).