1. **State the problem:** Solve the equation $-4x = 28$ 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 $-4$. 3. **Intermediate work:** $$-4x = 28$$ Divide both sides by $-4$: $$\frac{\cancel{-4}x}{\cancel{-4}} = \frac{28}{-4}$$ 4. **Simplify:** $$x = -7$$ 5. **Explanation:** Dividing both sides by $-4$ cancels the coefficient of $x$, leaving $x$ alone on the left side. Dividing $28$ by $-4$ gives $-7$, so the solution is $x = -7$. **Final answer:** $x = -7$