Absolute Value Calculator
Solve absolute value equations and inequalities with step-by-step solutions
Calculate Absolute Value
Formula:
|x| = x if x ≥ 0, |x| = -x if x < 0
Example: -15 or 3.14
Result:
Frequently Asked Questions
What is absolute value?
Absolute value is the distance a number is from zero on the number line, regardless of direction. It's always non-negative. |5| = 5 and |-5| = 5 because both are 5 units from zero.
How do you solve |x| = a?
For |x| = a where a ≥ 0, there are two solutions: x = a or x = -a. For example, |x| = 3 means x = 3 or x = -3. If a < 0, there's no solution since absolute value is never negative.
What about |x - 2| = 5?
Set up two equations: x - 2 = 5 or x - 2 = -5. Solving gives x = 7 or x = -3. Always check your solutions in the original equation to verify they work.
How do you solve |x| < a?
For |x| < a, the solution is -a < x < a (between -a and a). For |x| ≤ 3, the solution is -3 ≤ x ≤ 3, or [-3, 3] in interval notation.
How do you solve |x| > a?
For |x| > a, the solution is x < -a OR x > a (outside the interval). For |x| > 2, the solution is x < -2 or x > 2, written as (-∞, -2) ∪ (2, ∞).
Can absolute value be negative?
No, absolute value is always non-negative (positive or zero). The smallest possible absolute value is 0, which occurs only when the input itself is 0.