Using the properties of equality Find a solution to the equation 2f/5-8/5+2f=8

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will use the properties of equality.

1. **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:
\[
\frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8
\]

2. **Simplify the left side**: Combine the fractions:
\[
\frac{2f + 10f - 8}{5} = 8
\]
This simplifies to:
\[
\frac{12f - 8}{5} = 8
\]

3. **Eliminate the fraction**: Multiply both sides by 5 to eliminate the fraction:
\[
12f - 8 = 40
\]

4. **Isolate \(12f\)**: Add 8 to both sides:
\[
12f = 40 + 8
\]
This simplifies to:
\[
12f = 48
\]

5. **Solve for \(f\)**: Divide both sides by 12:
\[
f = \frac{48}{12}
\]
Therefore, we get:
\[
f = 4
\]

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