1. **State the problem:** Given the equation $12x - 21 = 11x - 9$, solve for $x$. 2. **Write the equation:** $$12x - 21 = 11x - 9$$ 3. **Isolate variable terms on one side:** Subtract $11x$ from both sides: $$12x - \cancel{11x} - 21 = \cancel{11x} - 9$$ $$x - 21 = -9$$ 4. **Isolate $x$ by adding 21 to both sides:** $$x - 21 + 21 = -9 + 21$$ $$x = 12$$ 5. **Final answer:** $$\boxed{12}$$ This means the value of $x$ that satisfies the equation is 12.