\( - \{ [ \pm \div 2 \times 7 ( 7 \times 2 + 1 ) ] - [ 8 \times 6 + 518 \div 3 ) \times 2 \} \)

To simplify the expression \( - \{ [ \pm \div 2 \times 7 ( 7 \times 2 + 1 ) ] - [ 8 \times 6 + 518 \div 3 ) \times 2 \} \), we first need to clarify the expression, as it contains some ambiguous symbols (like \( \pm \) and \( \div \) without clear operands). Assuming the expression is meant to be evaluated step by step, let's break it down: 1. **Evaluate the inner expressions**: - Calculate \( 7 \times 2 + 1 \): \[ 7 \times 2 = 14 \quad \text{so} \quad 14 + 1 = 15 \] - Calculate \( 518 \div 3 \): \[ 518 \div 3 = 172.6667 \quad \text{(approximately)} \] - Calculate \( 8 \times 6 \): \[ 8 \times 6 = 48 \] 2. **Substituting back into the expression**: - The first part becomes \( 7 \times 15 \): \[ 7 \times 15 = 105 \] - The second part becomes \( 48 + 172.6667 \): \[ 48 + 172.6667 = 220.6667 \] 3. **Putting it all together**: - Now we have: \[ - \{ [ \pm \div 2 \times 105 ] - [ 220.6667 \times 2 ] \} \] - Calculate \( 220.6667 \times 2 \): \[ 220.6667 \times 2 = 441.3334 \] 4. **Final expression**: - The expression now looks like: \[ - \{ [ \pm \div 2 \times 105 ] - 441.3334 \} \] - Since \( \pm \div 2 \) is ambiguous, we cannot proceed without clarification. If we assume it means \( + \) or \( - \), we can evaluate both cases. 5. **Assuming \( + \) for simplicity**: - If we take \( + \div 2 \) as \( + \): \[ 105 \div 2 = 52.5 \] - Then the expression becomes: \[ - \{ 52.5 - 441.3334 \} = - \{ -388.8334 \} = 388.8334 \] 6. **Assuming \( - \) for simplicity**: - If we take \( - \div 2 \) as \( - \): \[ -105 \div 2 = -52.5 \] - Then the expression becomes: \[ - \{ -52.5 - 441.3334 \} = - \{ -493.8334 \} = 493.8334 \] In conclusion, the final result depends on the interpretation of the ambiguous symbols. If you clarify the intended operations, I can provide a more precise answer.