Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Inequalities And Absolute Values
What Is Absolute Value?
The absolute value of a number is its distance from zero on the number line. Distance is always positive or zero, so absolute value is never negative.
| Expression | Meaning | Value | | |5| | distance from 0 to 5 | 5 | | |-5| | distance from 0 to -5 | 5 | | |0| | distance from 0 to 0 | 0 |
For any real number n: |n| = n if n ≥ 0, and |n| = -n if n < 0.
Absolute Value Inequalities
An absolute value inequality combines an absolute value with an inequality symbol. Solving these requires considering both the positive and negative possibilities.
Key Rules
| Inequality Form | Solution Form | Type | | |x| < a | -a < x < a | AND (intersection) | | |x| ≤ a | -a ≤ x ≤ a | AND (intersection) | | |x| > a | x < -a or x > a | OR (union) | | |x| ≥ a | x ≤ -a or x ≥ a | OR (union) |