To simplify the expression \( 5k - 8 + \frac{3}{5}(10k - 5) + 4k + 2 \), we'll follow these steps.
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Distribute \( \frac{3}{5} \) into \( (10k - 5) \): \[ \frac{3}{5}(10k - 5) = \frac{3}{5} \times 10k - \frac{3}{5} \times 5 = 6k - 3 \]
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Substitute the result of the distribution back into the expression: \[ 5k - 8 + (6k - 3) + 4k + 2 \]
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Combine the like terms. First, combine all the \( k \) terms: \[ 5k + 6k + 4k = 15k \]
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Now combine the constant terms: \[ -8 - 3 + 2 = -9 \]
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Putting it all together, we have: \[ 15k - 9 \]
Thus, the simplified expression is: \[ \boxed{15k - 9} \]
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