Linear Equation Calculator
Solve linear equations of the form ax + b = c for the unknown
variable x. The calculator shows each step — subtract b from both sides, then
divide by a — and reports the exact solution.
Enter coefficients
Enter a, b, c and press Solve for x.
Solving ax + b = c
x = (c − b) / a
Two algebraic steps:
- Subtract
bfrom both sides:ax = c − b. - Divide both sides by
a(a ≠ 0):x = (c − b) / a.
| Symbol | Meaning |
|---|---|
a | Coefficient of x (must be non-zero) |
b | Constant added to ax on the left side |
c | Total value on the right side |
x | The unknown we solve for |
Worked examples
Example 1 — Simple
Solve 3x + 5 = 20.
3x = 20 − 5 = 15, so x = 15 / 3 = 5.
x = 5
Example 2 — Negative coefficient
Solve −2x + 7 = 1.
−2x = 1 − 7 = −6, so x = −6 / −2 = 3.
x = 3
Example 3 — Decimal result
Solve 4x + 1 = 10.
4x = 9, so x = 9 / 4 = 2.25.
x = 2.25
Example 4 — No solution
Solve 0x + 5 = 20.
a = 0 makes the equation unsolvable — no value of x can make the left side equal to 20.
No solution
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Frequently asked questions
If a = 0 the equation is not linear in x — it becomes b = c. There is no value of x to solve for. The equation is either true for all x (if b = c) or false for all x (if b ≠ c).
Not when a ≠ 0. A non-degenerate linear equation has exactly one solution. Only equations of higher degree (like quadratics) can have multiple solutions.
Move all x terms to one side and all constants to the other. For example, from 3x + 5 = 2x + 10: subtract 2x from both sides → x + 5 = 10 → x = 5. This calculator handles the standard ax + b = c form; convert other forms to that shape first.