1. **State the problem:** Solve the equation $$r = x - y$$ for the variable $$x$$. 2. **Formula and rules:** To isolate $$x$$, we need to undo the subtraction of $$y$$ by adding $$y$$ to both sides of the equation. This uses the addition property of equality, which states that adding the same value to both sides keeps the equation balanced. 3. **Add $$y$$ to both sides:** $$r + y = x - y + y$$ 4. **Simplify the right side:** $$r + y = x + \cancel{- y} + \cancel{y}$$ 5. **Final expression for $$x$$:** $$x = r + y$$ **Answer:** $$x = r + y$$