1Cademy - Comparing Absolute Values and Integers

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Simplifying Absolute Value Expressions

Concept

Comparing Absolute Values and Integers

To compare numerical expressions involving absolute values, first simplify the absolute value expressions, then compare the resulting integers using inequality ( $<$ or $>$ ) or equality ( $=$ ) symbols. For instance, to compare $|-5|$ and $-|-5|$ , you first simplify both expressions: $|-5|$ simplifies to $5$ , and $-|-5|$ simplifies to $-5$ . Comparing these results yields $5 > -5$ , which means $|-5| > -|-5|$ . Similarly, to compare $-9$ and $-|-9|$ , simplify $-|-9|$ to $-9$ , which gives $-9 = -9$ , so $-9 = -|-9|$ . This principle applies to any pair of numbers.