Linear equation calculator (ax + b = c)
Solve first-degree equations in the form ax + b = c, with a check of the result.
How the calculation works
To isolate x in ax + b = c: move b to the other side (ax = c − b), then divide both sides by a: x = (c − b) ÷ a.
Example: 2x + 3 = 11 → 2x = 8 → x = 4. If x appears on both sides (e.g., 5x − 2 = 3x + 6), gather the x terms first: 2x = 8 → x = 4.
Examples
- 3x − 7 = 8 → 3x = 15 → x = 5.
- 5x − 2 = 3x + 6 → 2x = 8 → x = 4 (gathering the x terms).
Frequently asked questions
What if x is on both sides?
Add/subtract to gather the x terms on one side and the numbers on the other — the equation becomes ax + b = c and fits here.
How is it different from a quadratic?
In a linear equation the exponent of x is 1 and there is at most one solution. Quadratics (x²) have up to two — use the quadratic calculator.
Why does moving a term flip its operation?
Because you apply the same operation to both sides to keep the equality. Subtracting 3 from both sides is what makes a +3 "become −3" on the other side.
What if a is zero?
Then it is not a first-degree equation: without x, the equality is either always true (infinite solutions) or never (no solution).
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Updated on July 4, 2026 · by Rafael Rossi · Methodology & sources