To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will first eliminate the fractions by multiplying the entire equation by 5.
-
Multiply every term by 5: \[ 5 \left(\frac{2f}{5}\right) - 5 \left(\frac{8}{5}\right) + 5(2f) = 5(8) \]
This simplifies to: \[ 2f - 8 + 10f = 40 \]
-
Combine like terms: \[ (2f + 10f) - 8 = 40 \] \[ 12f - 8 = 40 \]
-
Add 8 to both sides: \[ 12f - 8 + 8 = 40 + 8 \] \[ 12f = 48 \]
-
Divide both sides by 12: \[ f = \frac{48}{12} \] \[ f = 4 \]
Thus, the solution to the equation is \( f = 4 \).