Quick answer
A linear equation ax + b = c has the solution x = (c − b) ÷ a. For 2x + 3 = 11, x = (11 − 3) ÷ 2 = 4.
Enter a, b and c. The calculator returns x.
Related tools: Linear Interpolation Calculator: Interpolate a value between two known points. Line Equation from Two Points Calculator: Equation of the line through two points. Slope Calculator: Slope, angle, distance and line equation through two points.
How to use the Linear Equation Calculator
- Enter a.
- Enter b.
- Enter c.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| a | A number | — |
| b | A number | — |
| c | A number | — |
Formula and method
Formula
x = (c − b) ÷ a
IEEE-754 double precision; shown to at most 6 decimal places.
Isolate x; a must not be 0.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: a = 2; b = 3; c = 11.
| Result | Value |
|---|---|
| x | 4 |
Example 2
Inputs: a = -5; b = 0; c = 10.
| Result | Value |
|---|---|
| x | -2 |
The first line is the headline result (x). IEEE-754 double precision; shown to at most 6 decimal places.
Check
Substitute back: 2(4) + 3 = 11 ✓. The steps are subtract b from both sides, then divide by a.
When a = 0
If a = 0 the equation has either no solution or every number as a solution, so a must be non-zero. For two unknowns you need a system of equations.
How the result changes with a
Holding every other input at the first worked example, this table changes only a. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| a | x |
|---|---|
| 1 | 8 |
| 2 | 4 |
| 4 | 2 |
| 8 | 1 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- a: entering "0" shows "a must not be 0." beside that field and no result.
Choosing between the Linear Equation Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Linear Interpolation Calculator](/math/linear-interpolation/) | x₁, y₁ and x₂ | Interpolated y |
| [Line Equation from Two Points Calculator](/math/line-equation-from-two-points/) | x₁, y₁ and x₂ | Equation |
| [Slope Calculator](/math/slope-calculator/) | x₁, y₁ and x₂ | Slope |
| [LCM Calculator](/math/lcm-calculator/) | numbers | Least common multiple |
| [Factor Calculator](/math/factor-calculator/) | number | Factors |
Background: algebra
Many algebra calculators rest on the same ideas: write the problem in a standard form, identify the coefficients, apply the formula and check the answer by substituting it back. For a quadratic ax² + bx + c = 0 the roots are (−b ± √(b² − 4ac)) ÷ 2a, and the discriminant b² − 4ac decides the kind of roots: positive gives two real roots, zero gives one repeated root and negative gives two complex conjugate roots.
If a = 0 the equation is linear, not quadratic. A sign slip on the −b term shifts both roots by the same amount, so substitute your roots back to check.
Assumptions and limitations
- a ≠ 0
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for a to confirm this.
Frequently asked questions
What is x in 5x − 10 = 15?
Add 10 to get 5x = 25, so x = 5.
What if the equation has x on both sides?
Move the x terms to one side first.
Is every linear equation solvable?
Yes, provided a ≠ 0: then x = (c − b) ÷ a has exactly one solution.
What does the Linear Equation Calculator calculate?
Solve ax + b = c for x. It returns x.
What formula does the Linear Equation Calculator use?
x = (c − b) ÷ a. Isolate x; a must not be 0.
What do I need to enter in the linear Equation Calculator?
You enter a, b and c.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. a ≠ 0.
What is an example of a linear Equation result?
With a 2, b 3 and c 11, the x is 4.
Related calculators
- Linear Interpolation Calculator — Interpolate a value between two known points.
- Line Equation from Two Points Calculator — Equation of the line through two points.
- Slope Calculator — Slope, angle, distance and line equation through two points.
- LCM Calculator — Least common multiple of two or more numbers.
- Factor Calculator — List every factor of a positive whole number.
- Quadratic Formula Calculator — Solve ax² + bx + c = 0, including complex roots.
- Rydberg Equation Calculator — Wavelength of a hydrogen spectral line between two energy levels.
- Net Ionic Equation Calculator — Balanced molecular, complete ionic and net ionic equations for common double-displacement reactions in water.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.