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How to Make an Absolute Value Inequality

Absolute value describes the quantity represented by a number without regard to its sign. One way to envision this is to picture a number line with zero in the center and numbers extending to its right and left. A number's absolute value is equal to its distance from zero on the number line. Just as a regular number can be greater than or less than another number, so an absolute value can be greater than or less than another absolute value. This comparison is expressed in an absolute value inequality.

Instructions

- 1
  Choose two quantities to compare. These can be constants, variables or equations.
  
  For example, you can compare 4 + 9 and x - 2, p and 3q, or 4 and -5.
- 2
  Decide which quantity has the greater absolute value.
  
  For instance, -5 has a greater absolute value than 4, because it is farther from zero on the number line.
- 3
  Place a greater than or less than sign between the two values. The sign should correctly identify the number with the greatest absolute value as "greater," even if it is a smaller number.
  
  For instance, -5 > 4.
- 4
  Place each quantity between two vertical lines to indicate absolute value.
  
  The finished equation is |-5| > |4|.

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