## Related Words

# 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="" 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

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=""><>
- Step 6: = x > 11 or x <>

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