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 ≥ 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

• Click here for samples
• Back to Mathematics Dictionary