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

Step 1: Start with the equation

$q - r = r$

Step 2: Move all terms involving $r$ to one side

Add $r$ to both sides of the equation to eliminate $r$ from the right side: $q = 2r$

Step 3: Solve for $r$

Now, divide both sides of the equation by 2: $r = \frac{q}{2}$

Final Answer:

$r = \frac{q}{2}$

Would you like any additional details or clarifications? Here are some related questions for further exploration:

1. How would you solve for $r$ if the equation was $q + r = 3r$?
2. How can you solve linear equations when terms involving the variable are on both sides?
3. What is the difference between solving linear and quadratic equations?
4. How do you check the solution to an equation like $q - r = r$?
5. Can you explain how to handle fractional coefficients in equations?

Tip: When solving linear equations, always try to isolate the variable by performing inverse operations step by step.