# Linear Equation Solver

URL: https://speedycalculator.com/calculators/math/linear-equation/
Last updated: 2026-10-25

> The linear equation solver finds x in an equation of the form ax + b = c. It also checks the answer by substituting it back into the equation.

## Inputs

- a
- b
- c

## Results

- x
- Check: a·x + b

## Formula

```
x = (c − b) ÷ a
```

## Explanation

A linear equation has one unknown to the first power. It always has exactly one solution unless a = 0.

### How to use the Linear Equation Solver

- **a**
- **b**
- **c**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Subtract b from both sides, then divide by a.

### Inputs explained

FieldWhat to enteraA numberbA numbercA number

### Example values

How the main result changes when **a** changes and everything else stays at the example values above:

ax21439.33334755.664.666783.5

## Worked example

Inputs — a: 4; b: -7; c: 21.

Results — **x = 7**; Check: a·x + b = 21.

## FAQ

**What if a = 0?**
There is no solution unless b = c, in which case every x works.

**How do I solve 3(x + 2) = 15?**
Expand to 3x + 6 = 15, so a = 3, b = 6, c = 15.

**What formula does the Linear Equation Solver use?**
x = (c − b) ÷ a.