1. **Problem 23:** Simplify the expression $7a - (5a + 1) + 15$. 2. **Problem 24:** Simplify the expression $-4(x + 5y) - 2(2y - 1x)$. --- ### Problem 23 1. Start with the expression: $$7a - (5a + 1) + 15$$ 2. Distribute the minus sign inside the parentheses: $$7a - 5a - 1 + 15$$ 3. Combine like terms: $$7a - 5a = 2a$$ 4. Combine constants: $$-1 + 15 = 14$$ 5. Final simplified expression: $$2a + 14$$ --- ### Problem 24 1. Start with the expression: $$-4(x + 5y) - 2(2y - 1x)$$ 2. Distribute $-4$ and $-2$: $$-4x - 20y - 4y + 2x$$ 3. Combine like terms for $x$: $$-4x + 2x = \cancel{-4x} + \cancel{2x} = -2x$$ 4. Combine like terms for $y$: $$-20y - 4y = -24y$$ 5. Final simplified expression: $$-2x - 24y$$