To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can follow these steps:
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Start with the equation: \[ \frac{2f}{5} - \frac{8}{5} + 2f = 8 \]
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Combine the terms involving \( f \). To do this, it is helpful to express \( 2f \) with the same denominator (which is 5). We can write \( 2f \) as \( \frac{10f}{5} \): \[ \frac{2f}{5} + \frac{10f}{5} - \frac{8}{5} = 8 \] This simplifies to: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]
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Next, add \( \frac{8}{5} \) to both sides of the equation: \[ \frac{12f}{5} = 8 + \frac{8}{5} \]
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To add the right side, we need a common denominator. The number 8 can be expressed as \( \frac{40}{5} \): \[ \frac{12f}{5} = \frac{40}{5} + \frac{8}{5} = \frac{48}{5} \]
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Now, multiply both sides by 5 to eliminate the denominator: \[ 12f = 48 \]
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Finally, divide both sides by 12 to solve for \( f \): \[ f = \frac{48}{12} = 4 \]
The solution to the equation is: \[ \boxed{4} \]