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

A) 4
B) 8/3
C) 12
D) 16/6

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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

1. Rewrite \( 2f \) in terms of fifths to combine it with \( \frac{2f}{5} \):
\[
2f = \frac{10f}{5}
\]
Substituting this into the equation gives:
\[
\frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8
\]

2. Combine the terms with \( f \):
\[
\frac{2f + 10f}{5} - \frac{8}{5} = 8
\]
This simplifies to:
\[
\frac{12f}{5} - \frac{8}{5} = 8
\]

3. To eliminate the fractions, multiply the entire equation by \( 5 \):
\[
5 \left( \frac{12f}{5} \right) - 5 \left( \frac{8}{5} \right) = 5 \times 8
\]
Simplifying this yields:
\[
12f - 8 = 40
\]

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

5. Finally, solve for \( f \) by dividing both sides by \( 12 \):
\[
f = \frac{48}{12} = 4
\]

The solution is \( f = 4 \).

So the answer is **A) 4**.