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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