To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can first combine like terms and then isolate \( f \).
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Combine the terms involving \( f \): \[ \frac{2f}{5} + 2f = \frac{2f}{5} + \frac{10f}{5} = \frac{2f + 10f}{5} = \frac{12f}{5} \] So now the equation looks like: \[ \frac{12f}{5} - \frac{8}{5} = 8 \]
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Next, let's eliminate the fractions by multiplying the entire equation by \( 5 \): \[ 5 \left( \frac{12f}{5} - \frac{8}{5} \right) = 5 \cdot 8 \] This simplifies to: \[ 12f - 8 = 40 \]
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Now, we can add \( 8 \) to both sides to isolate the term involving \( f \): \[ 12f = 40 + 8 \] \[ 12f = 48 \]
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Finally, we divide both sides by \( 12 \) to solve for \( f \): \[ f = \frac{48}{12} = 4 \]
Thus, the solution to the equation is \( f = 4 \).