1Cademy - Comparing Absolute Values and Integers

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Simplifying Absolute Value Expressions

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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.

Updated 2026-06-05

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OpenStax Intermediate Algebra

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Comparing $-8$ and $|-8|$
Comparing $-(-10)$ and $|-10|$
Comparing $8$ and $-|-8|$
Comparing $|-4|$ and $-|-4|$
Comparing $-(-16)$ and $|-16|$
Comparing $2$ and $-|-2|$
Comparing $-(-9)$ and $|-9|$
Comparing $7$ and $-|-7|$
Comparing $|-5|$ and $-|-5|$
Comparing $-9$ and $-|-9|$
Comparing $|-8|$ and $-|-8|$
Comparing $12$ and $-|-12|$
Comparing $|-6|$ and $-6$
Comparing $-(-15)$ and $-|-15|$
A supervisor at a logistics company is comparing two inventory adjustment values. Adjustment A is represented by $|-15|$ and Adjustment B is represented by $-|-15|$ . Which of the following symbols correctly compares the values of Adjustment A and Adjustment B?

$|-15|$ ____ $-|-15|$
An industrial technician is comparing two temperature readings from a cooling unit. Reading A is $-18$ degrees and Reading B is $-|{}-18|$ degrees. True or False: After simplifying the expressions, Reading A and Reading B represent the same numerical value.
An environmental scientist is comparing two water level readings relative to a fixed gauge. Reading A is $|-15|$ inches, and Reading B is $-|{}-15|$ inches. Arrange the following steps in the correct order to determine the mathematical relationship between these two readings.
A logistics manager is comparing stock level deviations to standard inventory targets. To prepare these values for comparison using inequality symbols, match each mathematical expression with its simplified integer value.
Comparing Inventory Deviations
An auditor is reviewing two numerical discrepancies in a corporate expense account to compare their overall impact. Discrepancy A is recorded as $|-25|$ and Discrepancy B is recorded as $-|-25|$ . Before determining which is greater, the auditor must simplify both expressions. The simplified integer value for Discrepancy B is ____.
Comparing Asset Benchmark Deviations

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