To simplify the expression \( 6(3x - 5) + 2(3x - 5) - 8(2x - 5) \), we can start by distributing the constants across the expressions in the parentheses:
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Distribute \(6\) and \(2\) in the first two terms: \[ 6(3x - 5) = 18x - 30 \] \[ 2(3x - 5) = 6x - 10 \]
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Now distribute \(-8\) in the third term: \[ -8(2x - 5) = -16x + 40 \]
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Now we can combine all the terms: \[ (18x - 30) + (6x - 10) + (-16x + 40) \]
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Combine like terms (combine the \(x\) terms and the constant terms):
- For the \(x\) terms: \[ 18x + 6x - 16x = 8x \]
- For the constant terms: \[ -30 - 10 + 40 = 0 \]
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Putting it all together: \[ 8x + 0 = 8x \]
So, the simplified expression is \(8x\).
The correct answer is 8x.