Linear Equation Solver
Solve a·x + b = c·x + d for x instantly.
How to use
- 1 Enter a (the x coefficient) and b (the constant) for the left side.
- 2 Enter c and d for the right side, or leave them at 0 for the a·x + b = 0 form.
- 3 Read the value of x, or the no-solution / infinite-solutions message.
- 4 Copy the answer for your working.
About Linear Equation Solver
The Linear Equation Solver finds the value of x in a first-degree equation of the form a·x + b = c·x + d, doing the algebra for you and showing what is going on under the hood.
Type the coefficient and constant on each side of the equals sign.
For a simple equation such as 2x + 4 = 0 you only need the left-hand fields; leave the right-hand coefficient and constant at zero.
For an equation with x on both sides, like 3x + 1 = x + 7, fill in all four boxes and the tool collects the x terms and the constants to reduce it to a single step.
The result shows the simplified form (coefficient times x equals constant) alongside the final value of x, so you can follow the reasoning rather than just copy an answer.
It also handles the awkward edge cases correctly.
If the x terms cancel and the constants match, every value of x works, so it reports infinitely many solutions; if the x terms cancel but the constants disagree, the equation is contradictory and it reports no solution.
Fractional answers are rounded to a sensible precision.
Everything is computed locally in your browser — no equations are uploaded, logged or stored — so it is private and keeps working offline once loaded, making it handy for homework, quick checks and teaching.
FAQ
What does “no solution” mean?
It means the x terms cancel out but the constants disagree, e.g. x + 1 = x + 2 reduces to 0 = 1, which can never be true, so no value of x satisfies the equation.
When does it report infinitely many solutions?
When both sides are identical after collecting terms, e.g. x + 2 = x + 2 reduces to 0 = 0, which holds for every x.
Can it solve quadratics or systems?
No, this tool handles single-variable linear (first-degree) equations. For ax² + bx + c = 0, use the quadratic equation solver instead.