1. **State the problem:** Solve the equation $-13x = -18$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ by dividing both sides of the equation by the coefficient of $x$, which is $-13$. 3. **Intermediate work:** $$-13x = -18$$ Divide both sides by $-13$: $$x = \frac{-18}{-13}$$ Simplify the fraction: $$x = \frac{18}{13}$$ 4. **Explanation:** Dividing both sides by $-13$ cancels out the coefficient on the left side, leaving $x$ alone. Since dividing two negative numbers results in a positive number, the solution is positive. **Final answer:** $$x = \frac{18}{13}$$