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Linear Equation Calculator: Solve ax + b = c Step by Step

Enter a, b and c for an equation of the form ax + b = c. You get x as an exact fraction, its decimal value and the working.

Solution

x = 5

Decimal value
5
Check: a·x + b
3·5 + 5 = 20
Show working
  1. 3x + 5 = 20
  2. 3x = 20 − 5 = 15
  3. x = 15 ÷ 3
  4. x = 5

How to use

  1. Write your equation as ax + b = c, e.g. 3x + 5 = 20.
  2. Enter a, b and c (negative numbers and decimals are fine).
  3. Read x and open “Show working” to see each step.

Good to know

Method: move b to the other side (ax = c − b), then divide both sides by a, so x = (c − b) ÷ a. The answer is shown as a fraction in lowest terms when it is one, e.g. x = 7/3 rather than 2.333…

If your equation has x on both sides, collect the x terms first. For 5x + 2 = 2x + 11, subtract 2x from both sides to get 3x + 2 = 11, then enter a = 3, b = 2, c = 11.

Special cases: if a = 0 there is no x left. Then either every x works (when b = c) or no x works (when b ≠ c). The calculator tells you which.

Questions

How do I solve 2x + 7 = 15?

Subtract 7 from both sides to get 2x = 8, then divide by 2: x = 4. Enter a = 2, b = 7, c = 15 to check.

Can the answer be a fraction?

Yes. 3x + 1 = 2 gives x = 1/3. The calculator shows the fraction and the decimal 0.333333.

What if there is x on both sides?

Bring all x terms to one side and the numbers to the other first, then enter the simplified a, b and c.

What does “no solution” mean?

With a = 0 the equation becomes b = c. If that is false (for example 0x + 2 = 5), no value of x can make it true.

Is my data stored or sent anywhere?

No. The calculation runs entirely in your browser; nothing you type leaves your device.

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