To simplify the expression \(6(3x−5)+2(3x−5)−8(2x−5)\), we will start by distributing each term.
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Distribute \(6\) and \(2\) into \(3x - 5\): \[ 6(3x - 5) = 18x - 30 \] \[ 2(3x - 5) = 6x - 10 \]
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Distribute \(-8\) into \(2x - 5\): \[ -8(2x - 5) = -16x + 40 \]
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Now, combine all the simplified expressions: \[ 18x - 30 + 6x - 10 - 16x + 40 \]
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Combine like terms (the \(x\) terms and the constant terms):
- For the \(x\) terms: \[ 18x + 6x - 16x = (18 + 6 - 16)x = 8x \]
- For the constant terms: \[ -30 - 10 + 40 = -30 - 10 + 40 = 0 \]
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Therefore, the entire expression simplifies to: \[ 8x + 0 = 8x \]
So, the simplified expression is \( \boxed{8x} \).
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