1. **State the problem:** Solve the equation $y - 7 = 12$ for $y$. 2. **Formula and rules:** To isolate $y$, add 7 to both sides of the equation. This is based on the addition property of equality which states that adding the same number to both sides keeps the equation balanced. 3. **Intermediate work:** $$y - 7 + 7 = 12 + 7$$ $$\cancel{y - 7} + 7 = 12 + 7$$ 4. **Simplify:** $$y = 19$$ 5. **Explanation:** We added 7 to both sides to cancel out the $-7$ on the left side, leaving $y$ alone. On the right side, we added 7 to 12, resulting in 19. **Final answer:** $y = 19$