To solve the equation \(\frac{2f}{5} - \frac{8}{5} + 2f = 8\), we will first combine like terms.
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Start with the equation: \[ \frac{2f}{5} - \frac{8}{5} + 2f = 8 \]
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To combine the terms, let's express \(2f\) in a fraction similar to \(\frac{2f}{5}\). We can rewrite \(2f\) as \(\frac{10f}{5}\) (since \(2f = \frac{10f}{5}\)): \[ \frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8 \]
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Now combine the \( \frac{2f}{5} \) and \( \frac{10f}{5} \): \[ \frac{2f + 10f}{5} - \frac{8}{5} = 8 \] \[ \frac{12f}{5} - \frac{8}{5} = 8 \]
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Combine the two fractions on the left-hand side: \[ \frac{12f - 8}{5} = 8 \]
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To eliminate the fraction, multiply both sides by \(5\): \[ 12f - 8 = 40 \]
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Now, isolate \(12f\) by adding \(8\) to both sides: \[ 12f = 40 + 8 \] \[ 12f = 48 \]
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Finally, solve for \(f\) by dividing both sides by \(12\): \[ f = \frac{48}{12} = 4 \]
Thus, the solution to the equation is: \[ \boxed{4} \]