Question

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

16/6
Start Fraction 16 over 6 End Fraction

4
4

12
12

8/3

Answer 1

To solve the equation \( \frac{2f}{5} - \frac{8}{5} + 2f = 8 \), we will simplify and isolate \( f \).

1. Combine like terms on the left side:

First, rewrite \( 2f \) in terms of fifths:
\[
2f = \frac{10f}{5}
\]
Now, the equation becomes:
\[
\frac{2f}{5} + \frac{10f}{5} - \frac{8}{5} = 8
\]
Combine \( \frac{2f}{5} + \frac{10f}{5} \):
\[
\frac{12f}{5} - \frac{8}{5} = 8
\]

2. To eliminate the fractions, multiply the entire equation by 5:
\[
5 \left( \frac{12f}{5} \right) - 5 \left( \frac{8}{5} \right) = 5 \cdot 8
\]

This simplifies to:
\[
12f - 8 = 40
\]

3. Now, isolate \( f \) by adding 8 to both sides:
\[
12f = 40 + 8
\]
\[
12f = 48
\]

4. Finally, divide both sides by 12:
\[
f = \frac{48}{12} = 4
\]

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

The correct response is:
**4**