﻿ Definition and examples absolute value | define absolute value - algebra 1 - Free Math Dictionary Online

# 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|.

• 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

### 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

#### 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=""><>
• Step 6: = x > 11 or x <>

Translate :

Please provide your email for a free trial as a Teacher or Student. This trial will be valid for the current academic year (2015-16). An email to this address includes the password to login to the full web application. You will also receive other promotional emails as and when such deals become available.

I am a Teacher Student