Question

using the properties of equality find the solution to the equation.
2f over 5- 8 over 5 + 2f=8

Answer 1

To solve the equation \(\frac{2f}{5} - \frac{8}{5} + 2f = 8\), let's begin by simplifying the equation step-by-step.

1. **Combine like terms**: First, let's focus on expressing \(2f\) with a common denominator. We can write \(2f\) as \(\frac{10f}{5}\).

The equation now looks like this:

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

2. **Combine the fractions on the left**:

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

This simplifies to:

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

3. **Eliminate the fraction**: Multiply both sides of the equation by 5 to eliminate the fraction:

\[
12f - 8 = 40
\]

4. **Isolate the term with \(f\)**: Add 8 to both sides:

\[
12f = 48
\]

5. **Solve for \(f\)**: Divide both sides by 12:

\[
f = 4
\]

Thus, the solution to the equation is:

\[
\boxed{4}
\]