1. **State the problem:** Solve the equation $x - 11 = 16 + 4x$ for $x$. 2. **Write down the equation:** $$x - 11 = 16 + 4x$$ 3. **Isolate the variable terms on one side:** Subtract $x$ from both sides: $$x - 11 - x = 16 + 4x - x$$ which simplifies to $$-11 = 16 + 3x$$ 4. **Isolate the constant terms on the other side:** Subtract 16 from both sides: $$-11 - 16 = 16 + 3x - 16$$ which simplifies to $$-27 = 3x$$ 5. **Solve for $x$ by dividing both sides by 3:** $$x = \frac{-27}{3} = -9$$ 6. **Final answer:** $$x = -9$$