1. **State the problem:** Simplify the expression $$\frac{10x - 5}{2x - 1} \times 10$$. 2. **Rewrite the expression:** The multiplication by 10 can be written as multiplication by $\frac{10}{1}$, so the expression becomes: $$\frac{10x - 5}{2x - 1} \times \frac{10}{1}$$ 3. **Multiply the numerators and denominators:** $$\frac{(10x - 5) \times 10}{(2x - 1) \times 1} = \frac{10(10x - 5)}{2x - 1}$$ 4. **Factor the numerator:** $$10(10x - 5) = 10 \times 5(2x - 1) = 50(2x - 1)$$ 5. **Substitute back:** $$\frac{50(2x - 1)}{2x - 1}$$ 6. **Cancel the common factor $2x - 1$:** $$\frac{50\cancel{(2x - 1)}}{\cancel{2x - 1}} = 50$$ **Final answer:** $$50$$