1. **Stating the problem:** Simplify the expression $$74 - \{6 + (-16) - (-16) + 25\}$$ step by step. 2. **Recall important rules:** - Multiplying two negative numbers results in a positive number. - Subtracting a negative number is equivalent to adding its positive. - Follow the order of operations: parentheses first, then addition and subtraction. 3. **Evaluate inside the braces step by step:** - Calculate $$6 + (-16) = -10$$ (as you correctly noted). 4. **Rewrite the expression:** $$74 - \{-10 - (-16) + 25\}$$ 5. **Simplify inside the braces further:** - Subtracting a negative: $$-10 - (-16) = -10 + 16 = 6$$ - Now add 25: $$6 + 25 = 31$$ 6. **Rewrite the expression:** $$74 - 31$$ 7. **Final subtraction:** $$74 - 31 = 43$$ **Final answer:** $$43$$