1. **Problem 1:** Simplify the expression $$-1.5(2m - 4) + 0.5(6m + 2)$$ 2. Use the distributive property: $$a(b + c) = ab + ac$$ 3. Distribute $$-1.5$$ and $$0.5$$: $$-1.5 \times 2m = -3m$$ $$-1.5 \times (-4) = +6$$ $$0.5 \times 6m = 3m$$ $$0.5 \times 2 = 1$$ 4. Substitute back: $$-3m + 6 + 3m + 1$$ 5. Combine like terms: $$-3m + 3m = \cancel{-3m} + \cancel{3m} = 0$$ $$6 + 1 = 7$$ 6. Final simplified expression for problem 1 is $$7$$. --- 7. **Problem 2:** Simplify the expression $$5(x + 2) - 3x$$ 8. Use distributive property: $$5 \times x = 5x$$ $$5 \times 2 = 10$$ 9. Substitute back: $$5x + 10 - 3x$$ 10. Combine like terms: $$5x - 3x = 2x$$ 11. Final simplified expression for problem 2 is $$2x + 10$$. **Answers:** - Problem 1: d. 7 - Problem 2: None of the given options (a. 8x + 2 is incorrect; correct is $$2x + 10$$)