Linear Equation Solver
This solver finds the single solution to any linear equation of the form ax + b = c. A linear equation is a polynomial equation of degree 1, where the variable x appears only to the first power. Every linear equation has exactly one solution (assuming a is not zero). This solver displays the step-by-step working, making it useful for learning algebra and verifying your manual solutions. Linear equations are fundamental in mathematics and appear in countless real-world applications, from physics and chemistry to economics and finance.",
How to solve a linear equation
To solve ax + b = c:
1. Start with: ax + b = c
2. Subtract b from both sides: ax = c - b
3. Divide both sides by a: x = (c - b) / a
Special case (ax + b = 0):
x = -b / a
Linear equations: frequently asked questions
What is a linear equation?
A linear equation is a polynomial equation of degree 1, with the general form ax + b = 0 or ax + b = c, where a and b are constants and a is not zero. Linear equations have exactly one solution for x. They are called linear because they represent a straight line when graphed.
How do I solve a linear equation?
To solve ax + b = c, isolate x by subtracting b from both sides (ax = c - b), then divide by a (x = (c - b) / a). For ax + b = 0, the solution is x = -b / a.
Can a linear equation have no solution?
For the form ax + b = c where a is not zero, there is always exactly one solution. However, if a is zero and b does not equal c, the equation has no solution. This solver requires a to be non-zero.
What does it mean to solve an equation?
To solve an equation means to find the value of the variable (in this case, x) that makes the equation true. Once you have found x, you can substitute it back into the original equation and verify that both sides are equal.
How do I use this solver?
Enter the coefficients a, b, and c for the equation ax + b = c. If you want to solve ax + b = 0, leave c as 0. The solver shows the step-by-step solution and displays the final answer for x.
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.