Linear Equation Calculator
This linear equation calculator solves any equation of the form ax plus b equals c for the unknown x, the most basic algebraic equation you will meet and one that underpins far more advanced maths. You enter three numbers: a, the coefficient that multiplies x; b, the constant added to it; and c, the value the expression must equal. The calculator instantly returns the solution x, along with a x, the value of the coefficient term once x is found, and a check figure showing a x + b recalculated, so you can confirm the answer satisfies the original equation. Working through equations like this by hand is slow and easy to get wrong with negative numbers or fractions, so this tool is useful for checking homework, revising algebra, or solving a real-world problem that reduces to a single linear equation, such as splitting a cost or working out a rate. If you enter zero for a, there is no x term left, so the calculator instead reports whether every value of x works, when b equals c, or whether no value of x can satisfy the equation, when b and c differ. Enter your own numbers, or try the worked example of 2x plus 3 equals 7, to see the method, the solution and the check calculated instantly as you type.
The formula
To solve ax + b = c, subtract b from both sides then divide by a: x = (c minus b) / a. This works whenever a is not zero.
Worked example
For 2x plus 3 = 7, subtract 3 to get 2x = 4, then divide by 2 to get x = 2. Enter 2, 3, 7 to confirm.
Frequently asked questions
How do I solve a linear equation?
Isolate the variable: move the constant to the other side, then divide by the coefficient. x = (c minus b) / a.
What if a is zero?
Then there is no x term. The equation is true for all x if b equals c, otherwise it has no solution.
Can it have more than one solution?
A genuine linear equation in one variable has exactly one solution, unless a is zero.
Who this calculator is for
This calculator is for algebra students and anyone needing a quick, reliable result.
What this calculator assumes
- You enter valid numbers.
- The standard method is applied.
- Results are rounded for display.
Formula and sources
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