Using the properties of equality, find the solution to the 2f

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can first combine like terms and then isolate \( f \).

1. 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:
\[
\frac{12f}{5} - \frac{8}{5} = 8
\]

2. 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:
\[
12f - 8 = 40
\]

3. Now, we can add \( 8 \) to both sides to isolate the term involving \( f \):
\[
12f = 40 + 8
\]
\[
12f = 48
\]

4. Finally, we divide both sides by \( 12 \) to solve for \( f \):
\[
f = \frac{48}{12} = 4
\]

Thus, the solution to the equation is \( f = 4 \).