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Math

Linear Equation Calculator

Solve ax + b = c, including identities and equations with no solution.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter coefficient a, constant b, right side c.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Subtract b from both sides. If a is nonzero, x = (c−b)/a. When a is zero, compare b and c to distinguish an identity from a contradiction.

A WORKED EXAMPLE

Using coefficient a = 3, constant b = 5, right side c = 20, the result is 5. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

The equation then says b = c. If this is true every real x works; otherwise no value of x can make it true.

What to keep in mind

One real variable and numeric coefficients. Floating-point arithmetic is used. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

What happens when the x coefficient is zero?

The equation then says b = c. If this is true every real x works; otherwise no value of x can make it true.

How can I check the result?

Subtract b from both sides. If a is nonzero, x = (c−b)/a. When a is zero, compare b and c to distinguish an identity from a contradiction. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.