1. **State the problem:** Simplify the expression $$\frac{18 - x}{3x - 1} \times \frac{7 - 21x}{2x - 36}$$. 2. **Rewrite each part by factoring where possible:** - Factor numerator and denominator where possible: $$18 - x = -(x - 18)$$ $$7 - 21x = 7(1 - 3x)$$ $$2x - 36 = 2(x - 18)$$ 3. **Rewrite the expression with factored terms:** $$\frac{-(x - 18)}{3x - 1} \times \frac{7(1 - 3x)}{2(x - 18)}$$ 4. **Notice that $1 - 3x$ can be rewritten as $-(3x - 1)$:** $$1 - 3x = -(3x - 1)$$ 5. **Substitute this into the expression:** $$\frac{-(x - 18)}{3x - 1} \times \frac{7 \times -(3x - 1)}{2(x - 18)} = \frac{-(x - 18)}{3x - 1} \times \frac{-7(3x - 1)}{2(x - 18)}$$ 6. **Multiply the numerators and denominators:** $$\frac{-(x - 18) \times -7(3x - 1)}{(3x - 1) \times 2(x - 18)}$$ 7. **Simplify the negatives:** $$-(x - 18) \times -7(3x - 1) = 7(x - 18)(3x - 1)$$ 8. **So the expression becomes:** $$\frac{7(x - 18)(3x - 1)}{2(3x - 1)(x - 18)}$$ 9. **Cancel common factors $(x - 18)$ and $(3x - 1)$:** $$\frac{7\cancel{(x - 18)}\cancel{(3x - 1)}}{2\cancel{(3x - 1)}\cancel{(x - 18)}} = \frac{7}{2}$$ **Final answer:** $$\boxed{\frac{7}{2}}$$