Linear Equation Solver (One Variable)

Solve any first-degree equation in one variable, such as 3(x − 2) + 5 = 2x + 11, and see each algebra step. Type it the way you would write it: brackets, division written with /, and coefficients next to the variable like 2x are all understood. The solver also recognises equations that have no solution or are true for every value.

How to use this tool

1. Type the equation with one equals sign, for example 5y − 7 = 2y + 1.
2. Use any single letter as the variable, and write multiplication as 2x, 2(x + 1) or 2*x.
3. Read the solution, its fraction form, and the check that both sides match.
4. Follow the steps table to see how the terms were collected.

Formula

ax + b = cx + d ⇒ x = (d − b) ÷ (a − c)

After brackets are expanded, every linear equation reduces to this form. If a = c the x terms cancel: when b = d as well the equation is true for every x, otherwise it has no solution. Decimal inputs and fractions use exact rational arithmetic, so tiny coefficients do not disappear. Variable products and denominators are rejected.

Example

For 3(x − 2) + 5 = 2x + 11, expanding the left side gives 3x − 6 + 5 = 3x − 1, so the equation becomes 3x − 1 = 2x + 11. Subtract 2x and add 1 on both sides to get x = 12. Check: 3(12 − 2) + 5 = 35 and 2 × 12 + 11 = 35.