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Enter values for a, b, and c, then solve the equation step by step.
What Is a Linear Equation?
A linear equation is an equation where the variable appears only to the first power. The standard form ax + b = c contains one variable, x, and three known numbers: a, b, and c. The goal is to find every value of x that makes the equation true.
Linear equations are the foundation of algebra. They appear in word problems, science formulas, budgeting, and any situation where two quantities change at a constant rate relative to one another. Being able to solve them quickly and check your work is a skill used from middle school through professional mathematics.
How to Solve ax + b = c
Special Cases in Linear Equations
Not every linear equation has exactly one solution. When a is zero, the equation no longer contains the variable x. In that case the equation becomes b = c. If b and c are the same number, the equation is true for every real number x, so there are infinitely many solutions. If b and c are different, the equation is never true, so there is no solution.
These special cases often surprise students, but they are easy to spot once you isolate the variable term. If the x term disappears and you are left with a true statement, every number works. If the x term disappears and you are left with a false statement, no number works.
Why Show the Steps?
Getting the final answer is only part of learning algebra. The steps reveal why the answer is correct and show how the equation changes as you apply each operation. Subtracting the same value from both sides keeps the equation balanced. Dividing both sides by the same non-zero value keeps the equation balanced. Each step is a small, justified move toward the solution.
Showing steps also makes it easier to find mistakes. If you accidentally add instead of subtract, the intermediate equation will look wrong. This calculator displays every transformation so you can compare it with your own work and understand the method rather than just copying the answer.
Common Linear Equation Examples
| Equation | Solution | Type |
|---|---|---|
| 2x + 3 = 7 | x = 2 | One solution |
| 5x - 4 = 11 | x = 3 | One solution |
| 0x + 5 = 5 | All real numbers | Infinite solutions |
| 0x + 5 = 3 | No solution | Contradiction |
Linear Equation FAQ
What is a linear equation? +
A linear equation is an equation where the variable is raised only to the first power. It can be written in the form ax + b = c, where a, b, and c are numbers and x is the variable.
How do I solve ax + b = c? +
Subtract b from both sides to isolate the term with x, giving ax = c - b. Then divide both sides by a to get x = (c - b) / a, as long as a is not zero.
What if a is zero? +
If a is zero, the x term disappears. The equation becomes b = c. If b equals c, every real number is a solution. If b does not equal c, there is no solution.
Can a linear equation have no solution? +
Yes. When a is zero and b does not equal c, the equation reduces to a false statement such as 0 = 2. No value of x can make it true.
Can a linear equation have infinitely many solutions? +
Yes. When a is zero and b equals c, the equation reduces to 0 = 0, which is true for every value of x.
How do I check my answer? +
Substitute your value of x back into the original equation and simplify both sides. If both sides are equal, your solution is correct.
External Resources
Authoritative references for linear equations and introductory algebra.
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