1. **State the problem:** Simplify the expression $$5(0.1x - 0.2) + 10x$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. This means we multiply each term inside the parentheses by the factor outside. 3. **Apply distribution:** $$5(0.1x - 0.2) = 5 \times 0.1x - 5 \times 0.2 = 0.5x - 1$$ 4. **Rewrite the expression:** $$0.5x - 1 + 10x$$ 5. **Combine like terms:** $$0.5x + 10x = (0.5 + 10)x = 10.5x$$ 6. **Final simplified expression:** $$10.5x - 1$$ This is the simplest form of the given expression.