1. We are given the inequality $$\frac{2 - x}{x - 2} > \frac{x}{x}$$ and the domain restriction $$1 \leq x < 3$$. 2. Notice that $$\frac{2 - x}{x - 2} = \frac{-(x - 2)}{x - 2} = -1$$ (for $$x \neq 2$$). 3. Also, $$\frac{x}{x} = 1$$ (for $$x \neq 0$$, which holds here since $$x \geq 1$$). 4. Substituting these simplifications, the inequality becomes $$-1 > 1$$. 5. This is false for all $$x$$ in the domain, so no solutions exist for $$1 \leq x < 3$$. Final answer: No solution for the inequality on the given interval.