Linear Equation Solver
Solve a one-variable linear equation ax + b = 0 and find the value of x.
The value of x that makes ax + b = 0.
Formula
Examples
| Input | Result |
|---|---|
| a = 2, b = -6 | x = 3 |
| a = 5, b = 10 | x = -2 |
About this calculator
A linear equation in one variable has the form ax + b = 0, where a and b are known constants and x is the unknown. As long as a is not zero, there is exactly one solution: x = −b ÷ a. You simply move the constant to the other side and divide by the coefficient of x.
There are two special cases. If a = 0 and b ≠ 0 the equation reduces to b = 0, which is false, so there is no solution. If both a = 0 and b = 0 the equation becomes 0 = 0, which is always true, meaning every number is a solution.
Frequently asked questions
Subtract b from both sides to get ax = −b, then divide both sides by a to get x = −b ÷ a, provided a is not zero.
If a = 0 the term with x disappears. With b ≠ 0 there is no solution, and with b = 0 every value of x works (infinitely many solutions).
Yes. Rewrite the equation so one side is 0 (here 3x − 6 = 0), then enter a = 3 and b = −6 to get x = 2.
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