Example

Comparing ∣−5∣|-5| and −∣−5∣-|-5|

To determine the relationship between ∣−5∣|-5| and −∣−5∣-|-5|, evaluate each expression separately. On the left side, the absolute value of −5-5 is 55, because its distance from zero is 55. On the right side, evaluate the absolute value first to get 55, and then apply the external negative sign, resulting in −5-5. Comparing these two integers, the positive value 55 is strictly greater than the negative value −5-5 (5>−55 > -5). By substituting the simplified integers with the original expressions, the final relationship is ∣−5∣>−∣−5∣|-5| > -|-5|.

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Updated 2026-06-03

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