Absolute Value Equation Solver
Solves modulus equations |ax+b|=c by splitting them into positive and negative cases. Visualizes solution intervals on a number line.
|x + | =
About
Absolute value represents the distance of a number from zero, regardless of direction. Therefore, an equation like |x| = 5 actually asks: "Which numbers are 5 units away from zero?" The answer involves two distinct cases: one positive and one negative. This tool splits the equation automatically. For inequalities, it determines whether the solution is a union of outer intervals or a single inner intersection, crucial for determining domains in calculus.
absolute value
modulus
inequalities
algebra
number line
Formulas
General Definition:
{
x if x ≥ 0−x if x < 0
Reference Data
| Type | Equation | Logic | Interval |
|---|---|---|---|
| Equality | |x| = a | x=a or x=-a | Points |
| Less Than | |x| < a | -a < x < a | (-a, a) |
| Greater Than | |x| > a | x < -a or x > a | (-∞, -a) U (a, ∞) |
| Zero | |x| = 0 | x = 0 | [0] |
| Negative | |x| = -5 | Impossible | Empty Set |
| Linear | |ax+b| = c | Two Linear Eqs | Two Points |
| Double | |x| = |y| | x=y or x=-y | Two Cases |
| Complex | |z| | Modulus | Magnitude |
Frequently Asked Questions
Because both 5 and -5 have a distance of 5 from zero.
The output of an absolute value function is always non-negative. However, the variable inside can be negative.
For y=|x-h|+k, the vertex is at (h, k), representing the turning point of the V-shape.