Algebra
Absolute Value Equation Solver
Solve equations involving absolute values. Solve equations of the form |ax + b| = c by breaking them into two separate equations and finding all possible solutions.
Examples:
Formula Reference
Linear Equation
ax + b = c → x = (c−b)/a
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Discriminant
Δ = b² − 4ac
Vertex Form
y = a(x−h)² + k
Share & Embed
Share your exact result or embed this tool.
Solution Methodology
01
Isolate Absolute Value
Move all other terms away from the absolute value expression.
02
Create Two Cases
Set the expression inside the bars equal to both the positive and negative value of the other side.
03
Solve Both Branches
Perform algebraic operations to find the values of x for both cases.
Common Questions
How do you solve an absolute value equation?
First, isolate the absolute value expression on one side. If the other side is a positive number c, split the equation into two cases: inside = c, and inside = -c. Solve both resulting equations to find all solutions.
Can an absolute value equation have no solution?
Yes. If the isolated absolute value expression equals a negative number (e.g., |x| = -5), there is no solution, because the absolute value of any real number is always non-negative.