✖️ Equation Solver
Solve linear equations of the form ax + b = c with step-by-step solutions.
What is this tool?
An equation solver is a mathematical tool designed to find the unknown variable in an algebraic equation. Linear equations of the form ax plus b equals c are among the most common types of equations encountered in school mathematics, science courses, and everyday problem-solving. Whether you are working through algebra homework, balancing a budget, converting recipes, or solving physics problems, linear equations appear everywhere. The variable x represents an unknown value that you need to find, while a, b, and c are known constants. For example, in the equation 3x plus 7 equals 22, the solver determines that x equals 5. Linear equations are called linear because when graphed on a coordinate plane, they produce a straight line. Understanding how to solve them manually is an essential skill, but having a reliable online solver lets you verify your work quickly and avoid careless arithmetic mistakes. This tool handles both integer and decimal inputs, and displays each intermediate step so you can follow the logical progression from the original equation to the final answer.How it works
The solver works by isolating the unknown variable x using standard algebraic operations. Starting with the equation ax plus b equals c, the first step is to subtract b from both sides, giving ax equals c minus b. The second step is to divide both sides by a, which yields x equals the quantity c minus b divided by a. This is the general solution formula. The tool performs these steps automatically and displays each one so you can verify the process. For example, with the equation 2x plus 6 equals 14, it first subtracts 6 from both sides to get 2x equals 8, then divides by 2 to arrive at x equals 4. If the coefficient a is zero, the equation becomes degenerate and the solver alerts you that no unique solution exists. The tool handles negative coefficients, fractional inputs, and equations where x appears on the right side.How to use
- Enter the coefficient a, which is the number multiplied by x. For example, in 3x plus 7 equals 22, the coefficient a is 3.
- Enter the constant b, which is the number added to or subtracted from the ax term. In the same example, b is 7.
- Enter the constant c, which is the value on the right side of the equation. In the example, c is 22.
- Press the Solve button to see the step-by-step solution and the final value of x.
- Verify your answer by substituting the value of x back into the original equation to make sure both sides are equal.
Frequently Asked Questions
Frequently Asked Questions
Can this solver handle quadratic equations?
No, this solver is designed for linear equations of the form ax plus b equals c, where the variable x has a power of 1. For quadratic equations involving x squared, you need a different tool or the quadratic formula. If you enter coefficients that result in a quadratic, the solver will not produce a valid result.
What happens if the coefficient a is zero?
If a equals zero, the equation becomes b equals c, which either has no solution if b and c are different values, or infinitely many solutions if they are equal. The solver will alert you that the equation is degenerate and cannot be solved for a unique value of x.
Does it support decimal and negative numbers?
Yes, the solver fully supports decimal inputs and negative coefficients. For example, you can solve negative 2.5x plus 3 equals 8, and the solver will correctly determine that x equals negative 2. Enter negative values directly using the minus sign.
Can I use fractions as coefficients?
Yes. Enter fractions as decimal values. For example, instead of one-half x equals 3, enter 0.5 for the coefficient a and the solver will find x equals 6. For more complex fraction arithmetic, use the fraction calculator alongside this tool.
Tips & Advice
Always double-check your equation before solving to make sure you have identified the correct coefficient and constants. If your equation has x on both sides, rearrange it first so all x terms are on the left and all constants are on the right. For example, 2x plus 5 equals x plus 11 should be rewritten as 1x plus 5 equals 11 before entering. When verifying your answer, substitute the value of x back into the original equation to confirm both sides match. This solver runs entirely in your browser, so no data is sent anywhere.