Linear Equation Calculator
Solve ax+b=cx+d with whole numbers, decimals or fractions. Follow the same operation on both sides and check the answer by substitution.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Subtract cx from both sides, subtract b from both sides, then divide by a−c if it is nonzero. Apply each operation to both sides to preserve equality. Finally substitute the solution into the original equation.
ax+b=cx+d → (a−c)x=d−b → x=(d−b)/(a−c), when a≠c
Worked example
3x+2=x+10. Subtract x from both sides: 2x+2=10. Subtract 2: 2x=8. Divide both sides by 2: x=4. Check: 3×4+2=14 and 4+10=14.
Assumptions and input details
Enter coefficients separately; do not paste a whole equation. Fractions such as -3/4 and decimals with up to six places are accepted. Coefficient magnitude is limited to 1e6 and reduced denominators to 1e6. Fraction operations and the solution are exact; displayed decimal approximations are rounded. If both x coefficients cancel, identical constants mean every real x is a solution; different constants mean no solution. The graph shows the two original sides only when the solution magnitude is at most 1e6.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Equation operations and fraction answers are exact. Decimal approximations and graph coordinates are rounded.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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