Math

Verified calculator with a transparent formula

Math

Linear Equation Calculator.

Solves a linear equation of the form ax + b = c for x, and shows the step-by-step solution.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Subtract b from both sides: ax = c - b.

  2. 2

    Divide both sides by a: x = (c - b) / a.

  3. 3

    Compute the result.

(c - b) / a

Frequently asked questions

What if a is zero?

If a = 0, the equation becomes b = c. If b = c, there are infinitely many solutions; otherwise, no solution. The calculator will show an error or undefined result.

Can I use decimals?

Yes, you can enter decimal values for a, b, and c. The calculator will handle them correctly.

What does the result represent?

It is the value of x that makes the equation ax + b = c true.

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How it works

Solves a linear equation of the form ax + b = c for x, and shows the step-by-step solution.

  1. Subtract b from both sides: ax = c - b.
  2. Divide both sides by a: x = (c - b) / a.
  3. Compute the result.

Formulas

The math behind this calculator, written out so you can verify the result.

Linear equation solution

x = (c - b) / a

To isolate x, subtract b from both sides and then divide by a.

Example:

Input: a = 2, b = 3, c = 7

Calculation: x = (7 - 3) / 2 = 4 / 2

Result: x = 2

Real-world use cases

Where this calculation shows up in everyday life.

Solving simple algebra problems

Quickly find the unknown in equations like 3x + 5 = 20.

Example: 3x + 5 = 20 → x = 5

Checking homework

Verify your manual solutions for linear equations.

Example: Check if x = 4 solves 2x - 1 = 7.

Understanding linear relationships

Find the input value that gives a desired output in a linear model.

Example: If y = 2x + 3 and y = 7, then x = 2.

Tips and common mistakes

Tips

  • Always check your answer by plugging x back into the original equation.
  • If a is negative, the solution will be negative or positive depending on the signs of b and c.
  • Use parentheses when entering negative numbers to avoid mistakes.

Common Mistakes to Avoid

  • Forgetting to subtract b from both sides before dividing.
  • Dividing by a without considering its sign.
  • Mixing up the order of operations when computing (c - b) / a.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.