Question

using the property of equality find the solution

2f/5 - 8/5 + 2f = 8

Answer 1

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

1. **Combine Like Terms:**

We can express \( 2f \) with a common denominator of 5:

\[
2f = \frac{2f \cdot 5}{5} = \frac{10f}{5}
\]

So the equation becomes:

\[
\frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8
\]

Combining the terms on the left side:

\[
\frac{2f + 10f - 8}{5} = 8
\]

This simplifies to:

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

2. **Eliminate the Fraction:**

To eliminate the fraction, multiply both sides by 5:

\[
12f - 8 = 40
\]

3. **Isolate the Variable \( f \):**

Add 8 to both sides:

\[
12f = 40 + 8
\]

\[
12f = 48
\]

Now, divide both sides by 12:

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

\[
f = 4
\]

So the solution to the equation is:

\[
\boxed{4}
\]