1. **State the problem:** Solve for $x$ in the equation $4x = 13x - 18$. 2. **Rewrite the equation:** Move all terms involving $x$ to one side to isolate $x$. $$4x - 13x = -18$$ 3. **Simplify the left side:** $$\cancel{4x} - 13x = -18$$ which simplifies to $$-9x = -18$$ 4. **Divide both sides by $-9$ to solve for $x$:** $$x = \frac{-18}{-9}$$ 5. **Simplify the fraction:** $$x = 2$$ **Final answer:** $x = 2$