Question

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

Answer 1

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

1. **Clear the fractions** by multiplying every term by 5:

\[
5 \left( \frac{2f}{5} \right) - 5 \left( \frac{8}{5} \right) + 5 (2f) = 5(8)
\]

This simplifies to:

\[
2f - 8 + 10f = 40
\]

2. **Combine like terms** on the left side:

\[
(2f + 10f) - 8 = 40
\]
\[
12f - 8 = 40
\]

3. **Isolate the term with \( f \)** by adding 8 to both sides:

\[
12f - 8 + 8 = 40 + 8
\]
\[
12f = 48
\]

4. **Solve for \( f \)** by dividing both sides by 12:

\[
f = \frac{48}{12}
\]
\[
f = 4
\]

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