1. **State the problem:** Find the limit $$\lim_{x \to 0} \frac{1 - 2x}{\frac{1}{x}}.$$\n\n2. **Rewrite the expression:** Dividing by a fraction is the same as multiplying by its reciprocal, so we have:\n$$\lim_{x \to 0} \frac{1 - 2x}{\frac{1}{x}} = \lim_{x \to 0} (1 - 2x) \times x.$$\n\n3. **Simplify the expression:** Multiply out the terms:\n$$\lim_{x \to 0} (x - 2x^2).$$\n\n4. **Evaluate the limit:** As $x$ approaches 0, both $x$ and $x^2$ approach 0, so:\n$$\lim_{x \to 0} (x - 2x^2) = 0 - 0 = 0.$$\n\n**Final answer:** $$0.$$