To solve the equation $q - r = r$ for $r$, follow these steps:

1. Start with the given equation: $q - r = r$

2. Add $r$ to both sides to eliminate $r$ on the right-hand side: $q = 2r$

3. Now, divide both sides of the equation by 2 to solve for $r$: $r = \frac{q}{2}$

Thus, the solution is: $r = \frac{q}{2}$

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What if the equation were $q + r = r$? How would the solution change?
2. How would the solution differ if the equation were $q - 2r = r$?
3. What happens if we introduce a constant, like $q - r = r + 1$?
4. How does solving for $r$ change if $q$ is negative?
5. Can this solution be visualized on a graph? If so, how?

Tip: When solving for a variable, aim to isolate it on one side of the equation by using inverse operations (addition, subtraction, etc.).