What is a linear equation calculator?
A linear equation calculator solves an equation where the variable appears only to the first power. This tool handles the general one-variable form ax + b = cx + d, including common special cases such as 3x + 5 = 20. For powers above one, use the Exponent Calculator for exponent arithmetic.
How does the linear equation calculator work?
The calculator subtracts cx from both sides and subtracts b from both sides, giving (a − c)x = d − b. If a − c is not zero, dividing both sides by a − c gives the unique solution.
What formula is used?
The Fraction Calculator can help if you want to work with fraction operations separately.
What do no solution and infinitely many solutions mean?
If a − c = 0 but d − b is not zero, the variable terms cancel and the equation becomes a false statement, so there is no solution. If both differences are zero, both sides are equivalent and every real value of x is a solution.
How do you use this linear equation calculator?
- Identify a and b on the left side.
- Identify c and d on the right side.
- Enter 0 for a missing coefficient or constant.
- Select Solve Equation and review the algebraic step and verification.
Linear equation examples
For 2x + 3 = 11, enter a = 2, b = 3, c = 0, d = 11; the solution is x = 4. For 3x + 2 = x + 10, x = 4. For 2x + 5 = 2x + 7, there is no solution. Ratio problems can often be simplified with the Ratio Calculator.
How is the solution verified?
When a unique solution exists, the calculator substitutes x into both ax + b and cx + d. The displayed verification shows the resulting left and right values so you can confirm they agree within floating-point tolerance.
What are the calculator's limits?
The inputs must be finite real numbers. Very large coefficients can exceed browser number limits. Decimal coefficients are supported, while exact fraction output is shown only when the reduced fraction can be derived safely from integer coefficients.
Frequently asked questions about linear equations
Methodology and calculation scope
The solution is classified using the combined coefficient a − c and combined constant d − b. A scale-aware floating-point tolerance is used only to distinguish values that are effectively zero after arithmetic; otherwise the direct algebraic result is preserved.