Let's solve the equation step by step:
Given the equation:
\[ \frac{2f}{5} - \frac{8}{5} + 2f = 8 \]
- First, combine the terms involving \(f\). Note that \(2f\) can be expressed with a common denominator of 5:
\[ 2f = \frac{10f}{5} \]
So, we rewrite the equation:
\[ \frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8 \]
- Now combine the \(f\) terms:
\[ \frac{2f + 10f}{5} - \frac{8}{5} = 8 \]
This simplifies to:
\[ \frac{12f}{5} - \frac{8}{5} = 8 \]
- To eliminate the fractions, multiply every term in the equation by 5:
\[ 5\left(\frac{12f}{5}\right) - 5\left(\frac{8}{5}\right) = 5 \cdot 8 \]
This simplifies to:
\[ 12f - 8 = 40 \]
- Next, add 8 to both sides:
\[ 12f = 40 + 8 \]
\[ 12f = 48 \]
- Finally, divide both sides by 12:
\[ f = \frac{48}{12} \]
Which simplifies to:
\[ f = 4 \]
Thus, the solution to the equation is:
\[ \boxed{4} \]