Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we can follow these steps:

1. **Combine like terms**:
We will first combine \( \frac{2f}{5} \) and \( 2f \). To do that, it helps to express \( 2f \) in terms of fifths:
\[
2f = \frac{10f}{5}
\]
Now, we can combine:
\[
\frac{2f}{5} + \frac{10f}{5} = \frac{12f}{5}
\]
So the equation becomes:
\[
\frac{12f}{5} - \frac{8}{5} = 8
\]

2. **Eliminate the fractions**:
To eliminate the fractions, multiply every term in the equation by 5:
\[
5 \left(\frac{12f}{5}\right) - 5 \left(\frac{8}{5}\right) = 5(8)
\]
Simplifying gives:
\[
12f - 8 = 40
\]

3. **Add 8 to both sides**:
\[
12f - 8 + 8 = 40 + 8
\]
This simplifies to:
\[
12f = 48
\]

4. **Divide both sides by 12**:
\[
f = \frac{48}{12}
\]
Simplifying gives:
\[
f = 4
\]

So, the solution to the equation is \( \boxed{4} \).