The given equation is:

\[
qf + pf = pq
\]

### Step 1: Isolate \( f \) on one side
First, move the term \( pf \) to the other side by subtracting \( pf \) from both sides:

\[
qf = pq - pf
\]

### Step 2: Factor out \( f \)
Now, factor out \( f \) on the right-hand side:

\[
f(q - p) = pq
\]

### Step 3: Solve for \( f \)
To solve for \( f \), divide both sides by \( q - p \) (assuming \( q \neq p \)):

\[
f = \frac{pq}{q - p}
\]

Thus, the solution is:

\[
f = \frac{pq}{q - p}
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions:
1. How would you solve for \( f \) if \( q = p \)?
2. How does the solution change if either \( q \) or \( p \) is 0?
3. What happens to the value of \( f \) as \( q \) approaches \( p \)?
4. Can this equation be solved using substitution methods? If yes, how?
5. What are some real-world applications of solving equations like this?

**Tip:** Always check for restrictions on variables, such as division by zero, to ensure valid solutions.

Learn how to solve the equation qf + pf = pq and isolate the variable f using basic algebraic techniques. This step-by-step solution walks through factoring and solving for a variable, making it suitable for students in Grades 9-12.

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