To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will use the properties of equality.
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Combine like terms: First, let's express \( 2f \) with a common denominator of 5: \[ 2f = \frac{10f}{5} \] So the equation can be rewritten as: \[ \frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8 \]
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Simplify the left side: Combine the fractions: \[ \frac{2f + 10f - 8}{5} = 8 \] This simplifies to: \[ \frac{12f - 8}{5} = 8 \]
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Eliminate the fraction: Multiply both sides by 5 to eliminate the fraction: \[ 12f - 8 = 40 \]
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Isolate \(12f\): Add 8 to both sides: \[ 12f = 40 + 8 \] This simplifies to: \[ 12f = 48 \]
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Solve for \(f\): Divide both sides by 12: \[ f = \frac{48}{12} \] Therefore, we get: \[ f = 4 \]
So, the solution to the equation is \( f = 4 \).
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