Linear Equation Solver
Solve equations of the form ax + b = 0
What is it?
This calculator solves linear equations of the form ax + b = 0, finding the single value of x that satisfies the equation.
Formula
ax + b = 0 → x = −b / a
Formula Explanation
Isolating x means moving the constant b to the other side (ax = −b) and then dividing both sides by a — a valid step as long as a is not zero, since division by zero is undefined.
Example Calculation
For 2x + 6 = 0 (a=2, b=6): x = −6 / 2 = −3.
How to Use
- Enter the coefficient a.
- Enter the constant b.
- Click Solve Equation to see the value of x.
Benefits
- Instantly handles all three cases: unique, infinite, or no solution.
- Shows the step-by-step rearrangement used to isolate x.
- Works for any real-number coefficients.
Use Cases
- Algebra homework involving single-variable linear equations.
- Quickly checking hand-solved equations for errors.
- Building blocks for solving systems of equations by substitution.
What Your Result Means
A unique solution means exactly one value of x satisfies the equation. Infinite solutions occur when the equation reduces to 0 = 0 (true for any x). No solution occurs when the equation reduces to a false statement, like 0 = 5.
Tips
- If a = 0, check whether b is also 0 to distinguish infinite solutions from no solution.
- Always double-check your sign when moving b to the other side of the equation.
- A linear equation graphs as a straight line, unlike a quadratic's curve.
Common Mistakes
- Forgetting to flip the sign of b when isolating x.
- Assuming a = 0 always means "no solution" without checking b as well.
- Confusing a linear equation (highest power of x is 1) with a quadratic (highest power is 2).
FAQs
What if a is 0?
If a = 0 and b = 0, every real number satisfies the equation (infinite solutions). If a = 0 and b isn't 0, no value of x can satisfy it (no solution).
What makes an equation "linear"?
A linear equation has variables raised only to the first power (no x², x³, etc.), which makes its graph a straight line.
How is this different from the Quadratic Equation calculator?
Linear equations have one solution (in the typical case), while quadratic equations (with an x² term) can have up to two solutions.
Can a linear equation have a negative solution?
Yes, if a and b have the same sign, x = −b/a will be negative.
What does "no solution" mean graphically?
It means the equation reduces to a contradiction (like 0 = 5), which has no corresponding point on the number line that satisfies it.
A unique solution is rounded to 4 decimal places.
Last updated: July 25, 2026