Linear Equation Solver
Solve one-variable linear equations with steps, fractions, parentheses, domain restrictions, and an answer check.
A linear equation is an equality where x appears only to the first power. The solver expands parentheses, combines like terms, isolates x, and flags denominator restrictions.
What a linear equation solver does
A linear equation has the variable only to the first power after the expression is simplified. This solver accepts a full equation, expands parentheses, combines like terms, moves variable and constant terms, then shows the value of x and checks the answer.
x is the unknown; a, b, and c are numeric coefficients in the original equation.
A is the collected coefficient of x and B is the constant term after moving all terms to one side.
Use this step when A is not zero.
- Expand parentheses and combine like terms
- Move x terms to one side and constants to the other
- Divide by the coefficient of x
- Substitute the answer back into the original equation
Fractions and domain restrictions
The solver supports numeric fractions and simple linear denominators. If a denominator can become zero, the calculator records the excluded value before multiplying both sides and checks the final answer against the original equation.
The value 3 is excluded because it makes the denominator zero.
Possible outcomes
| Condition | Result | Meaning |
|---|---|---|
| Coefficient of x is not zero | One solution | Solve for x directly |
| x cancels and the statement is true | Infinitely many solutions | Identity |
| x cancels and the statement is false | No solution | Contradiction |
Limits and related algebra tasks
This is not a full computer algebra system. It is designed for one variable and first-degree equations after simplification. If the expression contains x squared, products of two variable terms, or multiple unknowns, use a more specific solver.
- Use the linear inequality solver for less-than or greater-than signs
- Use a quadratic equation solver when x squared appears
- Use a system solver when there are two or more equations
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Solve one-variable linear inequalities with steps, sign-flip rule, interval notation, and a number line.
Solve quadratic equations from a full equation or standard coefficients. See the discriminant, real or complex roots, Vieta checks, excluded values, and a parabola graph.
Solve a 2x2 system of linear equations with Cramer's rule, determinants, solution classification, fractions, and substitution check.