Enter an equation (e.g., 2x+3=7)
- Enter your equation like 2x+3=7. × ÷ and full-width characters are normalized.
- Toggle options such as clearing denominators, verification, and fraction/decimal display.
- Click “Solve” to view the log, then copy a share URL, LaTeX, or SVG.
A one-line explanation under the result tells what the current step represents.
What does this output mean?
Multiply both sides by the LCM of denominators to turn coefficients into integers. The LCM is shown inside the log for fraction-heavy examples.
We remove x terms, move constants, and divide by the coefficient, always phrasing it as “do the same to both sides” to reduce sign mistakes.
When there is a unique solution, the value of x is substituted back into the original equation to show that both sides match.
FAQ
Why does applying the same operation keep the equation true?
Adding, subtracting, multiplying, or dividing both sides by the same value keeps the equality intact. The step log makes this visible.
How is this different from “transposing”?
Instead of flipping signs when moving terms, every step is a mirrored operation on both sides, which is safer with fractions or parentheses.
How do you clear denominators?
We compute the LCM of denominators and multiply both sides to make coefficients integers. The chosen LCM appears in the steps.
Are parentheses and implicit multiplication supported?
Yes. Inputs like 2x, 3(x-2), and (x+1)2 are normalized before solving.
How do you detect no solution or infinite solutions?
If the x coefficient becomes 0 and constants disagree, it is no solution; if they match, it is infinite solutions. Both are highlighted.
Is my input sent anywhere?
No. Everything stays in your browser; only copied share URLs contain your equation and options.
How to use Linear Equation Solver effectively
What this page is for
Use this page for one-variable linear equations such as 2x+3=7, 3(x-2)=12, or fractions on both sides. It rewrites the equation into the form ax+b=cx+d, then shows the same operation applied to both sides.
Input checks
Check signs, parentheses, and multiplication marks before solving. Full-width characters are normalized, but ambiguous expressions are easier to review when you write multiplication explicitly.
Workflow
Solve the equation, read each same-operation step, and keep denominator clearing turned on when fractions make the coefficients hard to compare. Use the verification line to substitute the answer back into the original equation.
Common mistakes
Do not treat a sign change as a shortcut without checking the operation that caused it. Also watch for equations where the x coefficient cancels to zero, because those can produce no solution or infinitely many solutions.
How to read the result
Read the status first. A unique solution gives the value of x, no solution means the simplified constants disagree, and infinite solutions means both sides simplify to the same expression.
Related calculators
Comments
Loaded only when you click. Until then, no external connection is made.