Zerdly

Linear Equation Solver

Solve a linear equation a·x + b = c for x, with the working shown.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

How to use this calculator

  1. Put your equation in the form a·x + b = c.
  2. Enter a (the coefficient of x), b (the constant on the left) and c (the right-hand side).
  3. Read the value of x.

How it works

A linear equation in one variable has the form a·x + b = c. Rearranging, x = (c − b) ÷ a.

If a = 0 there is no x term: the equation has no solution when b ≠ c, or infinitely many when b = c.

Worked example

2x + 3 = 11. x = (11 − 3) ÷ 2 = 8 ÷ 2 = 4.

Common mistakes

  • Not rearranging into a·x + b = c first — move all x terms to one side and constants to the other before entering values.
  • Entering a = 0, which leaves no x to solve for.

Frequently asked questions

How do you solve a linear equation for x?

Write it as a·x + b = c, then x = (c − b) ÷ a. For 2x + 3 = 11: x = (11 − 3) ÷ 2 = 4.

What if there is an x on both sides?

Collect the x terms on one side and the numbers on the other first. For example 5x + 2 = 2x + 11 becomes 3x = 9, so a = 3, b = 0 and c = 9, giving x = 3.

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Tip: Enter any known values to calculate the remaining results.

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