1. **State the problem:** Solve the equation $x^{-1} = -0.25$ for $x$. 2. **Recall the meaning of negative exponents:** $x^{-1} = \frac{1}{x}$. 3. **Rewrite the equation using this rule:** $$\frac{1}{x} = -0.25$$ 4. **To solve for $x$, multiply both sides by $x$ to get rid of the denominator:** $$\cancel{x} \times \frac{1}{\cancel{x}} = -0.25 \times x$$ $$1 = -0.25x$$ 5. **Now isolate $x$ by dividing both sides by $-0.25$:** $$\frac{1}{\cancel{-0.25}} = \frac{-0.25x}{\cancel{-0.25}}$$ $$x = \frac{1}{-0.25}$$ 6. **Calculate the division:** $$x = -4$$ **Final answer:** $$\boxed{-4}$$