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Bot GPT 4-o mini To solve the equation \(\frac{2f}{5} - \frac{8}{5} + 2f = 8\), we will first combine like terms.
1. Start with the equation:
\[
\frac{2f}{5} - \frac{8}{5} + 2f = 8
\]
2. To combine the terms, let's express \(2f\) in a fraction similar to \(\frac{2f}{5}\). We can rewrite \(2f\) as \(\frac{10f}{5}\) (since \(2f = \frac{10f}{5}\)):
\[
\frac{2f}{5} - \frac{8}{5} + \frac{10f}{5} = 8
\]
3. Now combine the \( \frac{2f}{5} \) and \( \frac{10f}{5} \):
\[
\frac{2f + 10f}{5} - \frac{8}{5} = 8
\]
\[
\frac{12f}{5} - \frac{8}{5} = 8
\]
4. Combine the two fractions on the left-hand side:
\[
\frac{12f - 8}{5} = 8
\]
5. To eliminate the fraction, multiply both sides by \(5\):
\[
12f - 8 = 40
\]
6. Now, isolate \(12f\) by adding \(8\) to both sides:
\[
12f = 40 + 8
\]
\[
12f = 48
\]
7. Finally, solve for \(f\) by dividing both sides by \(12\):
\[
f = \frac{48}{12} = 4
\]
Thus, the solution to the equation is:
\[
\boxed{4}
\]