The answer and how it was reached
Solves ax + b = c, shows the working step by step and substitutes the answer back as a check.
A linear equation takes two moves: shift the constant to the right, then divide by the coefficient. Both steps are printed, because for schoolwork the write-up matters as much as the answer.
The degenerate cases are handled properly too. When the coefficient is zero the equation either has no solution or holds for every x — and that is a correct answer, not an error.
What this calculator shows
- The value of x as a decimal and as a fraction
- The working with your numbers substituted in
- A check that puts the answer back into the original equation
What to keep in mind
- The equation must be in the form ax + b = c; collect terms in x on the left first.
- With a = 0 and b = c any number works; with a = 0 and b ≠ c nothing does — both are reported explicitly.
FAQs
What if x appears on both sides?
Collect the x terms on the left and the numbers on the right. 5x + 3 = 2x + 12 becomes 3x + 3 = 12, so a = 3, b = 3, c = 12.
Why can a = 0 give infinitely many solutions?
Because x disappears from the equation. If what remains is true, every number works; if false, none does.
How do I handle brackets?
Expand and collect like terms first, then rearrange into ax + b = c. This solver works on the tidied form.
How is this different from a quadratic?
A linear equation has x only to the first power and exactly one root. A quadratic has x² and can have two roots, one or none — there is a separate solver for that.
Worked example
3x + 5 = 20
Input: a=3, b=5, c=20
Output: x = 5
Note: Working: 3x = 20 − 5 = 15, so x = 15 ÷ 3. Check: 3 × 5 + 5 = 20.