Absolute Value
Definition of 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|.
More about Absolute Value
- 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 x for x ≥ 0
- Absolute Value Inequalities:
For all real numbers x and y, y > 0,
1. if |x | < y, then – y < x < y
2. if |x | > y, then x > y or x < - y
- 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
Solved Example on Absolute Value
Simplify the inequality |6 - x| - 3 > 2.
Choices:
A. x < -11 or x > - 1
B. x > 11 or x < 1
C. x < 11 or x > 1
D. None of these
Correct Answer: B
Solution:
Step 1: |6 - x| - 3 > 2 = |6 - x|> 5
Step 2: = - 5 > 6 - x > 5
Step 3: = - 5 - 6 > - x > 5 - 6
Step 4: = - 11 > - x > - 1
Step 5: = 11 < x < 1
Step 6: = x > 11 or x < 1
Related Terms for Absolute Value
- Absolute Value Function
- Piecewise Function
- Absolute Value Equation
- Absolute Value Inequality
- Number Line
Additional Links for Absolute Value
