Absolute Value

Absolute Value of a number is its distance from zero on the number line. The absolute value of a number n is denoted by |n|.

Absolute value function is a piecewise function and is written as f (x) = |x|, where f(x) ≥ 0 for all values of x
This means that f (x) = - x for x < 0="" or="" f="" (x)="x" for="" x="" ≥="">
Absolute Value Inequalities: For all real numbers x and y, y > 0
1. if |x| < y,then="" -y="">< x=""><>
2. if |x| > y, then x > y or x <>
Absolute Value Equation: It is an equation of the form |ax + b| = c

Examples of Absolute Value

Absolute Value: The absolute value of – 5 is 5, because – 5 is 5 units away from zero on the number line.
The absolute value of 6 is 6, because 6 is 6 units away from zero on the number line.
Absolute Value Function: y = |x| + 3
Absolute Value Inequalities: |m| > 5
Absolute Value Equation: |x - 3| = 6

Video Examples: Absolute Value 1

Solved Example on Absolute Value

Simplify the inequality |6 - x| - 3 > 2

Choices:

A. x < -="" 11="" or="" x=""> - 1
B. x > 11 or x <>
C. x < 11="" or="" x=""> 1
D. None of these