Example

Comparing −1-1 and ∣−1∣|-1|

To determine the relationship between −1-1 and ∣−1∣|-1|, simplify the absolute value expression on the right side. The absolute value of −1-1 corresponds to its distance from zero, which is 11 (∣−1∣=1|-1| = 1). After simplification, the comparison is directly between the negative integer −1-1 and the positive integer 11. Since any negative number is always positioned to the left of a positive number on the number line, −1<1-1 < 1. Consequently, the complete statement is −1<∣−1∣-1 < |-1|. This exercise reinforces the principle that a negative number is always strictly smaller than the absolute value of any non-zero integer.

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Updated 2026-06-17

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