To solve for \( q_2 \) in the equation:

\[
q_1 = p \cdot (q_2 - q_1)
\]

Follow these steps:

1. Distribute the \( p \) on the right-hand side:

\[
q_1 = p \cdot q_2 - p \cdot q_1
\]

2. Add \( p \cdot q_1 \) to both sides to isolate the \( p \cdot q_2 \) term:

\[
q_1 + p \cdot q_1 = p \cdot q_2
\]

3. Factor out \( q_1 \) on the left-hand side:

\[
q_1 \cdot (1 + p) = p \cdot q_2
\]

4. Finally, divide both sides by \( p \) to solve for \( q_2 \):

\[
q_2 = \frac{q_1 \cdot (1 + p)}{p}
\]

This is the solution for \( q_2 \).

Would you like more details or have any questions about this? Here are some related questions:

1. What is the general method for solving linear equations?
2. How does factoring work in algebraic expressions?
3. Can this equation be applied to real-world problems like economics?
4. What are the steps to check if a solution is correct?
5. How would this equation change if there were more terms?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure accuracy.

Learn how to solve the linear equation q1 = p (q2 - q1) step-by-step. This problem involves algebraic manipulation and is suitable for Grades 7-9 students studying linear equations.

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