Example

Comparing ∣−4∣|-4| and −∣−4∣-|-4|

To compare the expressions ∣−4∣|-4| and −∣−4∣-|-4|, evaluate both sides separately. For the left side, the absolute value of −4-4 is 44. For the right side, evaluate the absolute value first to get 44, and then apply the external negative sign, resulting in −4-4. Comparing the two simplified integers on the number line, the positive value 44 is greater than the negative value −4-4 (4>−44 > -4). As a result, the correct relationship is ∣−4∣>−∣−4∣|-4| > -|-4|. This comparison highlights the structural difference between an absolute value and its direct opposite.

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Updated 2026-06-03

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