Absolute Value
Find the distance of a number from zero on the number line.
Always returns a non-negative result.
The Formula
|x| = x if x ≥ 0, |x| = -x if x < 0
The absolute value of a number is its distance from zero, regardless of direction. It strips away the sign, always giving a non-negative result.
Variables
| Symbol | Meaning |
|---|---|
| |x| | Absolute value of x (always ≥ 0) |
| x | Any real number |
Example 1
Solve |2x - 6| = 10
Case 1: 2x - 6 = 10 → 2x = 16 → x = 8
Case 2: 2x - 6 = -10 → 2x = -4 → x = -2
x = 8 or x = -2
Example 2
Find the distance between -7 and 4 on the number line
Distance = |(-7) - 4| = |-11|
Distance = 11
When to Use It
Use absolute value when:
- Finding the distance between two numbers
- Expressing error or deviation (always positive)
- Solving equations and inequalities with absolute values
- Working with magnitudes regardless of direction