Linear equation calculator
Solves ax + b = c and shows every step.
Fill in the fields and the result will appear here automatically.
Solves the numerical equation ax + b = c by moving b, dividing by a and showing substitution of the calculated x. At a = 0 the question becomes b = c: if true, every real x works; otherwise there is no solution. Both cases are meaningful answers. For x on both sides, collect the coefficients before entering them.
How it works
Formula and logic
x = (c − b) ÷ a whenever a is not zero; if a is zero the equation reduces to comparing b with c.
Example
For 3x + 5 = 20, moving 5 gives 3x = 15 and dividing gives x = 5.
Fields and units
- Coefficient a — unitless
- Constant b — unitless
- Right-hand side c — unitless
How to use
- — Enter the coefficient in front of x.
- — Enter the constant term and the right-hand side.
- — Read the root and the steps.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: linear equations, identities and no-solution cases
- Limitation
- Enter finite numerical coefficients, including zero and negative values. Steps and substitution are rounded to six significant digits; small and large values use scientific notation. Substitution is a numerical check, not proof that the rounded text is exact. The calculation stops if a displayed intermediate result or x falls outside the number range.
FAQ
What happens when the coefficient is zero?
The x term disappears and the equation becomes b = c. If that is true, every number is a root; if not, there is none.
Are negative coefficients supported?
Yes, all three values may be negative or fractional. The sign is carried through the division.
Why show a substitution check?
Substituting the calculated x helps check signs and rearrangement. The row is rounded, so a visible equality does not prove last-digit accuracy. Check the original coefficients algebraically when an exact fractional answer is needed.
Can it solve quadratics?
No, this is degree one only. A separate calculator handles equations with an x squared term.