1. **State the problem:** Simplify the expression $$- \{3 + [-(-9) \cdot 4 - 6 \div 3]\} + 5 \cdot 2 \cdot [7 - 10] \div 3$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). 3. **Simplify inside the innermost brackets:** - Calculate $-(-9) = 9$. - Then multiply: $9 \cdot 4 = 36$. - Divide: $6 \div 3 = 2$. - So inside the square brackets: $36 - 2 = 34$. 4. **Simplify inside the curly braces:** - Add: $3 + 34 = 37$. - So the expression becomes: $$- \{37\} + 5 \cdot 2 \cdot [7 - 10] \div 3$$. 5. **Simplify inside the square brackets:** - Calculate $7 - 10 = -3$. 6. **Calculate the multiplication and division:** - Multiply: $5 \cdot 2 = 10$. - Multiply: $10 \cdot (-3) = -30$. - Divide: $$\cancel{(-30)} \div \cancel{3} = -10$$. 7. **Put it all together:** - The expression is now: $$-37 + (-10)$$. 8. **Final addition:** - Calculate: $-37 - 10 = -47$. **Final answer:** $$-47$$