math

Linear Equation Solver

Solve a·x + b = c instantly — handles unique solutions, no solution, and infinitely many solutions.

a (coefficient of x)

b (constant on left)

c (right-hand side)

Solution of a·x + b = c

x = 2

x = (c − b) ÷ a = (7 − 3) ÷ 2

How it works

1Enter coefficients a and b (left side) and the right-hand side value c to define the equation a·x + b = c.
2The solver computes x = (c − b) ÷ a when a ≠ 0, and detects degenerate cases (a = 0) where there is either no solution or infinitely many.
3The result panel shows the solution and a full arithmetic breakdown so you can verify every step.

Checking algebra homework — enter the equation coefficients and confirm your hand-calculated answer.
Engineering and science problems where a single unknown appears linearly, such as Ohm’s law rearrangements.
Teaching tool: students can explore how changing a, b, or c shifts the solution and why a = 0 is a special case.

What does no solution mean?

When a = 0 and b ≠ c the equation reduces to a false statement (e.g. 3 = 7), so no real number x can satisfy it.

What does infinitely many solutions mean?

When a = 0 and b = c the equation reduces to a true identity (e.g. 5 = 5), which holds for every value of x.

Can I enter decimal or negative values?

Yes — a, b, and c accept any real number including negatives and decimals. The solver handles all cases exactly.

Calculate the area and perimeter of a rectangle from its width and height, with a labeled diagram.

Calculate the area and circumference of a circle from its radius, with a labeled diagram.

Calculate the area (Heron’s formula) and perimeter of a triangle from its three sides.

Calculate the area and perimeter of a trapezoid from its two parallel sides, height, and legs.