Absolute value |x| represents the distance of x from zero on the number line, always non-negative. |5| = 5, |−5| = 5. It 'strips the sign' from a number. In geometry, |a−b| gives the distance between two points on a number line.
How to Use
Enter any number or expression:
- Single: |−42| = 42
- Distance: |a − b|
- Equation: |2x + 3| = 7
Properties
- |x| ≥ 0 always
- |x| = 0 iff x = 0
- |−x| = |x|
- |a × b| = |a| × |b|
- |a + b| ≤ |a| + |b| (triangle inequality)
Solving |ax+b| = c
If c ≥ 0: two cases. ax+b = c OR ax+b = −c. If c < 0: no solution. Example: |2x−4| = 6 → 2x−4=6 (x=5) or 2x−4=−6 (x=−1).
Step-by-Step Instructions
- 1Enter a number.
- 2View its absolute value.
- 3Check the distance from zero.
- 4Try absolute value equations.
- 5Explore batch calculations.