To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will first combine like terms and isolate \( f \).
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Rewrite \( 2f \) in terms of fifths to combine it with \( \frac{2f}{5} \): \[ 2f = \frac{10f}{5} \] Substituting this into the equation gives: \[ \frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8 \]
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Combine the terms with \( f \): \[ \frac{2f + 10f}{5} - \frac{8}{5} = 8 \] This simplifies to: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]
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To eliminate the fractions, multiply the entire equation by \( 5 \): \[ 5 \left( \frac{12f}{5} \right) - 5 \left( \frac{8}{5} \right) = 5 \times 8 \] Simplifying this yields: \[ 12f - 8 = 40 \]
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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 \( 12 \): \[ f = \frac{48}{12} = 4 \]
The solution is \( f = 4 \).
So the answer is A) 4.