Evaluate: . (This is the opposite of the opposite of .)
- (correct answer)
Explanation: This question tests evaluating the opposite of an opposite, which always returns to the original number due to the property -(-a) = a. The expression -(-7) means "the opposite of the opposite of 7": first we find the opposite of 7 (which is -7), then find the opposite of that result (-7), which gives us 7. For example, -(-3) = 3 (opposite of -3 is 3), -(-10) = 10 (opposite of -10 is 10), and this pattern -(-a) = a works for any number. Evaluating -(-7): the inner negative makes 7 become -7, then the outer negative makes -7 become 7, so -(-7) = 7. Common errors include thinking double negatives stay negative (-(-7) = -7), adding the values (-(-7) = -14), or confusing with zero. The key insight is that applying the opposite operation twice returns you to where you started: if you flip a number's sign twice, you get back the original number. This fundamental property helps simplify expressions and understand that negation is its own inverse operation.