1. **State the problem:** Simplify the expression $7 - \{6 - 12 \div (5 + 9 \times 2 - 19)\}$. 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 parentheses:** Calculate $5 + 9 \times 2 - 19$. - First multiply: $9 \times 2 = 18$. - Then add and subtract: $5 + 18 - 19 = 23 - 19 = 4$. 4. **Rewrite the expression:** $7 - \{6 - 12 \div 4\}$. 5. **Divide:** $12 \div 4 = 3$. 6. **Simplify inside the braces:** $6 - 3 = 3$. 7. **Final subtraction:** $7 - 3 = 4$. **Answer:** The simplified value is $4$.