Linear Equation Solver (ax+b=0)
Enter coefficients a and b to solve the linear equation ax+b=0. Get x=−b/a instantly, including the special cases when a is zero.
Last updated:
Input
Enter the coefficients a and b of the linear equation ax+b=0 to find the solution x=−b/a.
x +
= 0
Both a and b can be any real number. Setting a to 0 triggers the no-solution or infinite-solution case.
Result
Solution
x = 3
Because a is not zero, the solution is uniquely determined.
Coefficient a
2
Coefficient b
-6
Formula
x = −b ÷ a
How it works
- A linear equation ax+b=0 is solved by subtracting b from both sides and dividing by a, giving x=−b/a.
- When the coefficient a is not zero, there is exactly one solution, x=−b/a.
- When a is zero and b is also zero, every real number satisfies the equation, so there are infinitely many solutions.
- When a is zero and b is not zero, no value of x can satisfy the equation, so there is no solution.
- The number line is a visual aid that shows where the solution x lies.
Frequently asked questions
- How is the linear equation ax+b=0 solved?
- You subtract b from both sides and divide by a, giving x=−b/a. For example, 2x+6=0 gives x=−6/2=−3.
- What happens when the coefficient a is zero?
- If a=0 and b=0, every real number satisfies the equation, so the solution is indeterminate (infinitely many). If a=0 and b≠0, no value of x works, so there is no solution.
- Can it handle fractional or decimal answers?
- Yes. Since it computes x=−b/a directly, non-integer results are shown as decimals, and the number line diagram shows roughly where x sits.
Reviews
Tell us what you think of this calculator.
Write a review
Found an incorrect result or a problem? Turn this on to report it.
Rating