1. **State the problem:** Simplify the expression $$\frac{6 - 18x}{2} \times \frac{5}{1 - 3x}$$. 2. **Rewrite the expression:** $$\frac{6 - 18x}{2} \times \frac{5}{1 - 3x}$$ 3. **Factor where possible:** Notice that $6 - 18x$ can be factored as $6(1 - 3x)$. So the expression becomes: $$\frac{6(1 - 3x)}{2} \times \frac{5}{1 - 3x}$$ 4. **Simplify the fraction:** $$\frac{\cancel{6}(1 - 3x)}{\cancel{2}} \times \frac{5}{1 - 3x} = 3(1 - 3x) \times \frac{5}{1 - 3x}$$ 5. **Cancel common factors:** The $(1 - 3x)$ terms cancel out: $$3 \cancel{(1 - 3x)} \times \frac{5}{\cancel{(1 - 3x)}} = 3 \times 5$$ 6. **Multiply remaining terms:** $$3 \times 5 = 15$$ **Final answer:** $$15$$