Question

Using the properties of equality, find the solution to the equation \frac{2f}{5}-\frac{8}{5}+2f=8.(1 point) Responses 12 12 4 4 \frac{16}{6} Start Fraction 16 over 6 End Fraction \frac{8}{3}

Answer 1

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

1. First, combine like terms. Rewrite \(2f\) as \(\frac{10f}{5}\) to get a common denominator:

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

This simplifies to:

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

2. To eliminate the fraction, multiply both sides by 5:

\[
12f - 8 = 40
\]

3. Next, isolate the term with \(f\) by adding 8 to both sides:

\[
12f = 48
\]

4. Finally, divide both sides by 12:

\[
f = 4
\]

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

So, the response is **4**.