To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can follow these steps:
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Combine like terms: We will first combine \( \frac{2f}{5} \) and \( 2f \). To do that, it helps to express \( 2f \) in terms of fifths: \[ 2f = \frac{10f}{5} \] Now, we can combine: \[ \frac{2f}{5} + \frac{10f}{5} = \frac{12f}{5} \] So the equation becomes: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]
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Eliminate the fractions: To eliminate the fractions, multiply every term in the equation by 5: \[ 5 \left(\frac{12f}{5}\right) - 5 \left(\frac{8}{5}\right) = 5(8) \] Simplifying gives: \[ 12f - 8 = 40 \]
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Add 8 to both sides: \[ 12f - 8 + 8 = 40 + 8 \] This simplifies to: \[ 12f = 48 \]
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Divide both sides by 12: \[ f = \frac{48}{12} \] Simplifying gives: \[ f = 4 \]
So, the solution to the equation is \( \boxed{4} \).