To solve the equation \(2f \cdot \frac{5 - 8}{5} + 2f = 8\), let's start simplifying it step by step.
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Simplify the expression \(2f \cdot \frac{5 - 8}{5}\): \[ 5 - 8 = -3 \implies 2f \cdot \frac{-3}{5} \]
Thus, the original equation can be rewritten as: \[ 2f \cdot \frac{-3}{5} + 2f = 8 \] This simplifies to: \[ -\frac{6f}{5} + 2f = 8 \]
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Now, combine like terms: To combine \(-\frac{6f}{5}\) and \(2f\), we rewrite \(2f\) with a common denominator: \[ 2f = \frac{10f}{5} \] Therefore, we have: \[ -\frac{6f}{5} + \frac{10f}{5} = 8 \] This simplifies to: \[ \frac{4f}{5} = 8 \]
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Now, isolate \(f\) by multiplying both sides by 5: \[ 4f = 40 \]
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Divide both sides by 4: \[ f = 10 \]
Thus, the solution to the equation is: \[ \boxed{10} \]
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