How do you solve ax + b = 0?

Move b to the other side: ax = -b, then divide both sides by a. The formula is x = -b / a.

When does a linear equation have infinitely many solutions?

If a = 0 and b = 0, the equation becomes 0 = 0, so there are infinitely many solutions.

When does a linear equation have no solution?

If a = 0 and b ≠ 0, the equation becomes impossible, for example 5 = 0, so there is no solution.

Can I enter decimal coefficients?

Yes, the calculator supports both integers and decimal numbers.

Linear Equation Solver

Solve equations in the form ax + b = 0, find x, see a step-by-step explanation, and handle special cases.

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Enter coefficients

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a·x + b = 0

Coefficient a

Coefficient b

Examples of linear equations

Result

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Enter coefficients and click “Calculate”.

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Linear Equation Solver — How It Works

This calculator helps you solve linear equations in the form ax + b = 0. It finds the value of x, shows the main transformation steps, and explains special cases.

Linear Equation Form

The standard form is: ax + b = 0, where a and b are numbers and x is a variable.

How to find x

To solve the equation:

move b to the right side: ax = -b
divide both sides by a: x = -b / a

Special cases

If a = 0, the variable x disappears from the equation.

a = 0, b = 0 — infinitely many solutions
a = 0, b ≠ 0 — no solution

Example

For the equation 2x − 8 = 0:

2x = 8
x = 8 / 2 = 4

When to use this calculator

This calculator is suitable for simple first-degree equations with one variable. For quadratic equations, use a separate quadratic equation calculator.

Frequently Asked Questions

What is a linear equation?

It is a first-degree equation, for example ax + b = 0.

What is the formula for x?

If a ≠ 0, then x = -b / a.

What happens if a = 0?

Then the equation does not contain x. It either has no solutions or infinitely many solutions.

When are there infinitely many solutions?

When a = 0 and b = 0, the equation becomes 0 = 0.

When is there no solution?

When a = 0 and b ≠ 0, the equation becomes impossible, for example 7 = 0.

Can I enter decimal numbers?

Yes, the calculator supports both integer and decimal coefficients.