Algebra Solver
Every linear equation of the form ax + b = c reduces to the same three-line solution. This tool skips straight to x, which is useful for checking homework or a quick real-world rearrangement without redoing the algebra by hand.
Inputs
Result
x = 5
How it works
x = (c − b) ÷ a
- 13x + 5 = 20
- 23x = 15
- 3x = 5
How the algebra solver works
Rearranging ax + b = c gives x = (c − b) ÷ a.
If a = 0, the equation either has no solution (b ≠ c) or is true for every x (b = c) — either way, there is no single unique answer, which is why the tool flags this case instead of dividing by zero.
Worked example: 3x + 5 = 20
- 3x + 5 = 20.
- 3x = 20 − 5 = 15.
- x = 15 ÷ 3 = 5.
Common mistakes to avoid
Entering a = 0 and expecting a numeric answer
With a = 0 the x term vanishes entirely, so there's no coefficient to divide by — the equation is either always true or never true, not solvable for a single x.
Mixing up which side b belongs on
This solver assumes the standard form ax + b = c. If your equation is written differently (e.g. b on the right with a sign flip already applied), rearrange it into this form first or the sign of x will come out wrong.
Frequently asked questions
What if my equation has x on both sides, like 2x + 3 = x + 9?
Move all x terms to one side by hand first: 2x − x + 3 = 9 becomes x + 3 = 9, which is a = 1, b = 3, c = 9 in this tool's form.
Can this solve quadratics or equations with x²?
No — for anything with x² use the Quadratic Equation Solver, which handles the discriminant and complex roots this linear tool can't.
Why does it say 'no unique solution' sometimes?
That happens when a = 0. If b also equals c the equation is true for all x; if not, it has no solution at all.
Does it handle fractional or negative coefficients?
Yes, a, b and c can be any real numbers including negatives and decimals.
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