1. **State the problem:** Solve the equation $x - 10 = 20$ for $x$. 2. **Formula and rules:** To isolate $x$, add 10 to both sides of the equation. This uses the addition property of equality which states that adding the same number to both sides keeps the equation balanced. 3. **Intermediate work:** $$x - 10 + 10 = 20 + 10$$ 4. **Simplify:** $$x + \cancel{-10} + \cancel{10} = 30$$ 5. **Final answer:** $$x = 30$$ This means the value of $x$ that satisfies the equation is 30.