Linear Equation Solver

ax + b = 0 → x = −b / a. Single-variable linear equations in standard form.

Inputs

Result

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How to use this calculator

  • Enter a and b.
  • Read x.

About this calculator

A linear equation in one variable has the form ax + b = 0; solution x = −b/a (provided a ≠ 0). When a = 0, the equation degenerates: if b = 0, every real number is a solution; if b ≠ 0, no solution. Linear equations are the foundation of algebra — every other equation type extends or specializes them. Used in conversions, simple physics (constant velocity), and as a step inside more complex solves (e.g. Gaussian elimination).

Frequently asked

Why a ≠ 0?+
If a = 0, equation isn't actually linear — it's either always true or never true.
What about ax + b = c?+
Rewrite as ax + (b − c) = 0. Set b' = b − c.
Slope-intercept form?+
y = mx + b. Setting y = 0 to find x-intercept becomes ax + b = 0 with a = m.
Why is this trivial calculator useful?+
For students learning algebra. Also handles 0a = 0b edge cases that some calculators get wrong.
Multi-variable linear?+
Two variables: see systems-of-equations-2x2. Three+ variables: matrix methods (Gaussian elim).

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