What This Tool Does
Enter one equation with the variable x. The calculator displays the original equation, one combined-form step, the formula and substitution lines, and the result.
For a unique numeric solution, the result includes a reduced exact fraction when needed and a decimal value. An identity is reported as infinitely many solutions; a contradiction is reported as no solution.
How to Use the Linear Equation Calculator
- Enter an equation in the field labeled Linear equation.
- Click Solve, or press Enter while the field is active.
- Review the Result section and its Steps list.
- Use Copy result or Download result (.txt) to save the displayed result.
- Click Reset to clear the equation and result.
Result Types
- The equation has exactly one variable,
x, and is degree 1 (nox^2or higher). - Coefficients can be integers, decimals, or fractions written as a division (e.g.
1/2 x); the calculator tracks them as exact fractions internally. - If
a = 0andb is not zero, the equation is an identity - true for every value ofx- so there is no single numeric solution. - If
a = 0andb is not zero, the equation is a contradiction - never true - so there is no solution. - The calculator solves the algebra as entered; it does not infer units or real-world context.
Supported Input
Use the fixed expression parser to enter numbers, x, the operators + - * / ^, and parentheses. The input is parsed as an expression; it is not executed as code.
- Variable:
xonly. - Implicit multiplication:
2x,3(x + 1), and2(x + 1)are all understood as multiplication. - Fractions and decimals: write a fraction as a division, like
1/2 xorx/3, or use a decimal like0.5x. - Exponents: use a non-negative whole-number constant after
^.x^1is permitted; variable-containing exponents are not. - Equals sign: include exactly one
=, with a non-empty expression on each side.
How the Result Is Determined
After parsing, the calculator combines both sides into ax + b = 0, where a is the coefficient of x and b is the constant. It then applies x = -b / a.
- If
ais not zero, the tool shows the exact solution and a decimal approximation when the value is not a whole number. - If
a = 0andb is not zero, the equation is an identity and has infinitely many solutions. - If
a = 0andbis not zero, the equation is a contradiction and has no solution.
Limits and Error Messages
The equation can contain up to 200 characters. Exponents above 12 are not supported. After parsing, any degree greater than 1, including x^2 or higher, is rejected.
Errors also appear for unsupported symbols, malformed syntax, unbalanced parentheses, a missing or multiple = signs, an expression containing x in a denominator, or division by zero. The tool does not solve inequalities, systems of equations, or higher-degree equations.
Privacy and Local Calculation
The equation is parsed and calculated in your browser. The tool's script.js contains no upload of the entered equation.
Frequently Asked Questions
What is a linear equation?
A linear equation in one variable is an equation where the highest power of the variable is 1, such as 2x + 3 = 7 or 3(x - 1) = 2x + 4. Once simplified, it can always be written in the form ax + b = 0.
What formula does this calculator use?
After moving every term to one side and combining like terms, the equation is in the form ax + b = 0. The calculator isolates x using x = -b / a. If a is 0, it reports whether the equation is always true (identity) or never true (contradiction) instead of a single value.
What notation can I type?
Numbers, the variable x, the operators + - * / ^, and parentheses. Implicit multiplication is understood, so 2x, 3(x+1), and 2(x+1) all work. Fractions can be entered as a division, like 1/2 x, and decimals like 0.5x are accepted too.
Does the calculator execute my input as code?
No. Your equation is parsed by a fixed expression parser that recognizes numbers, the variable x, the operators + - * / ^, and parentheses. It does not evaluate arbitrary code. Unsupported symbols or expressions produce an error instead of a result.
What if my equation has x squared or higher?
This calculator is dedicated to linear (degree 1) equations only. If your equation contains x^2 or a higher power, it will tell you the degree it found instead of guessing at a wrong answer - use a quadratic or general algebra solver for those equations.