Math

Linear Equation Solver

Solve a one-variable linear equation of the form ax + b = c.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

x
x
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Check: a·x + b
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Linear Equation Solver by TheCalcTools

How the Linear Equation Solver works

Enter the coefficient a, the constant b and the right-hand side c of ax + b = c.

The calculator subtracts b from both sides, then divides both sides by a.

The check row substitutes the answer back into the left side; it should equal c.

The formula

ax + b = cx = (c − b) ÷ a

Worked example

Using the default values shown in the calculator:

a (coefficient of x)3
b (constant)5
c (right-hand side)20
  1. The equation is 3x + 5 = 20. Subtract 5 from both sides: 3x = 15.
  2. Divide by 3: x = 5.00.
  3. Check: 3 × 5.00 + 5 = 20.00.

Result:

x5.0000
Check: a·x + b20.0000

Frequently asked questions

What if a is zero?

Then the equation becomes b = c. It is either always true (no unique x) or never true, so there is no single solution for x.

Can the answer be negative or a fraction?

Yes. If c is smaller than b, or if a does not divide c − b evenly, x will be negative or a decimal.

Sources and further reading

System of Equations Calculator (2×2)Solve a system of two linear equations, a₁x + b₁y = c₁ and a₂x + b₂y = c₂ Quadratic Equation SolverSolve any quadratic equation ax² + bx + c = 0 and see the discriminant, both roots and… Cubic Equation Calculator (Solve ax³ + bx² + cx + d = 0)Enter the four coefficients to find every root Complex Number Calculator (Add, Multiply, Divide, Polar Form)Enter two complex numbers a + bi and c + di and choose the operation Exponential Growth and Decay CalculatorEnter the starting value, rate and time Parabola Calculator (Vertex, Focus, Directrix, Vertex Form)Enter the coefficients a, b and c

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