Let's solve the equation \( 8 + 5f = -4f + 1 + 8f \) for \( f \).

### Step 1: Combine like terms on both sides
On the left side, there are no like terms to combine, so it stays the same:
\[
8 + 5f
\]
On the right side, combine the terms involving \( f \):
\[
-4f + 8f = 4f
\]
So the equation simplifies to:
\[
8 + 5f = 1 + 4f
\]

### Step 2: Move the terms involving \( f \) to one side of the equation
Subtract \( 4f \) from both sides:
\[
5f - 4f + 8 = 1
\]
This simplifies to:
\[
f + 8 = 1
\]

### Step 3: Solve for \( f \)
Subtract 8 from both sides:
\[
f = 1 - 8
\]
\[
f = -7
\]

So, the solution is \( f = -7 \).

Would you like more details or have any questions? 

Here are five related questions to further explore the topic:
1. How do you solve an equation when \( f \) appears on both sides?
2. What happens if the terms involving \( f \) cancel out?
3. Can you solve a similar equation, \( 3f + 2 = 2f - 5 \)?
4. How do you check if your solution is correct in this context?
5. What are the steps to solve equations involving fractions?

**Tip:** Always simplify the equation step by step to avoid mistakes and make the solution process easier.

Learn how to solve the equation 8 + 5f = -4f + 1 + 8f step-by-step with detailed explanations. This problem covers equations and combining like terms, suitable for students in Grades 7-9.

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