Calxsolver
Algebra

Linear Equation Solver

A linear equation in one variable has the form mx + b = c. The solver isolates x by subtracting b from both sides and dividing by m, showing each operation. It also handles the special cases where m = 0, which give either no solution or infinitely many.

Linear Equation Solver

Solve mx + b = c for x with each algebra step shown.

Try:
Answerx = 2
  1. Equation2x + 3 = 7
  2. Subtract b2x = 7 − (3) = 4
  3. Divide by mx = 4 / 2 = 2
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Formula and method

mx + b = c → x = (c − b) / m

Subtract b from both sides to get mx = c − b, then divide both sides by m to isolate x. Two degenerate cases are handled: when m = 0 and b = c the equation has infinitely many solutions; when m = 0 and b ≠ c there is no solution.

Worked examples

Solve 3x + 7 = 22 Isolate the unknown in a linear equation step by step. Solve 2x − 9 = 5 Solve a linear equation with subtraction on the left-hand side.

Key terms

Coefficient A constant multiplier in front of a variable or a term of a polynomial.

Frequently asked questions

What form of equation does this accept?

It solves mx + b = c. Rearrange other linear equations into this shape, collecting the variable on the left.

What happens when m is 0?

The variable disappears: the equation has infinitely many solutions when b = c, and no solution otherwise.

Can the answer be a fraction?

Yes. The result is shown as an exact decimal, rounded only to remove floating-point noise.

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