1. **State the problem:** Solve for $x$ in the equation $x - 3 = 2$. 2. **Formula and rules:** To isolate $x$, add 3 to both sides of the equation to cancel out the $-3$. 3. **Intermediate work:** $$x - 3 + 3 = 2 + 3$$ $$x + \cancel{-3} + \cancel{3} = 5$$ 4. **Simplify:** $$x = 5$$ 5. **Explanation:** Adding 3 to both sides keeps the equation balanced and removes the $-3$ from the left side, leaving $x$ alone. **Final answer:** $x = 5$