Question

Question
Using the properties of equality, find the solution to the equation 2f/5−8/5+2f=8 .(1 point)
Responses

83
Start Fraction 8 over 3 End Fraction

166
Start Fraction 16 over 6 End Fraction

4
4

12
12

Answer 1

Let's solve the equation step by step:

Given the equation:

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

1. First, combine the terms involving \(f\). Note that \(2f\) can be expressed with a common denominator of 5:

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

So, we rewrite the equation:

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

2. Now combine the \(f\) terms:

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

This simplifies to:

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

3. To eliminate the fractions, multiply every term in the equation by 5:

\[
5\left(\frac{12f}{5}\right) - 5\left(\frac{8}{5}\right) = 5 \cdot 8
\]

This simplifies to:

\[
12f - 8 = 40
\]

4. Next, add 8 to both sides:

\[
12f = 40 + 8
\]

\[
12f = 48
\]

5. Finally, divide both sides by 12:

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

Which simplifies to:

\[
f = 4
\]

Thus, the solution to the equation is:

\[
\boxed{4}
\]