Linear Equation Calculator

This linear equation calculator solves a one variable linear equation of the form ax plus b equals c. Enter the three numbers and the calculator returns the value of x that makes the equation true, along with a check. Linear equations are the simplest and most common equations in algebra: the unknown appears to the first power only, and there is exactly one solution as long as the coefficient a is not zero. If a is zero the equation either holds for every x or for none, and the calculator reports that. The method, a worked example and the assumptions are below.

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a x =

Check (a x + b)

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

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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