Sign up
Linear Equation calculator →

Linear Equation guide

The Linear Equation Solver isolates the variable x in an equation of the form ax + b = c. It also gracefully handles special cases where there are infinite solutions or no solution at all.

Worked examples

Solve a standard equation (2x + 5 = 15)

  1. Enter 2 as the coefficient (a).
  2. Enter 5 as the constant (b).
  3. Enter 15 as the result (c).
  4. Click Solve Equation.
Result: x = 5

Subtract 5 from both sides to get 2x = 10, then divide by 2 to find x = 5.

Solve an equation with a negative constant (3x - 6 = 9)

  1. Enter 3 as the coefficient (a).
  2. Enter -6 as the constant (b).
  3. Enter 9 as the result (c).
  4. Click Solve Equation.
Result: x = 5

Add 6 to both sides to get 3x = 15, then divide by 3 to find x = 5.

Identify an equation with infinite solutions

  1. Enter 0 as the coefficient (a).
  2. Enter 5 as the constant (b).
  3. Enter 5 as the result (c).
  4. Click Solve Equation.
Result: Infinite solutions (Identity)

The equation becomes 0x + 5 = 5, which simplifies to 5 = 5. Because this is always true, any value of x works.

Tips

  • •If the coefficient (a) is 0, the equation is no longer linear and the calculator will check for identities or contradictions.
  • •You can enter decimals and fractions using the decimal equivalent (e.g., 0.5 for 1/2).
  • •Always double-check by plugging your answer for x back into the original equation.

Frequently asked questions

What is a linear equation?
An equation where the highest power of the variable is 1. When graphed, it forms a straight line.
What is the standard form ax + b = c?
It is a common way to write a linear equation, where a is the coefficient, b is a constant, and c is the result.
What does "Infinite solutions" mean?
It means any number you plug in for x will make the equation true. This happens when both sides of the equation are identical (e.g., 5 = 5).
What does "No solution" mean?
It means there is no number that can make the equation true. This happens when you get a false statement like 5 = 10.
Why does the calculator give an error if a = 0?
If a = 0, the x variable disappears. The equation becomes b = c. The calculator doesn't throw a math error, but it tells you it is either an identity or a contradiction.
Can I solve equations with fractions?
Yes, but you should convert fractions to decimals first (e.g., 1/2 becomes 0.5) before entering them into the fields.
How do I solve a linear equation manually?
Subtract b from both sides (c - b), then divide that result by a. The formula is x = (c - b) / a.
What is a coefficient?
The number multiplying the variable. In 2x, the coefficient is 2.
Can a linear equation have two solutions?
No. A linear equation can have exactly one solution, infinite solutions, or no solution. It cannot have exactly two.
What is an identity equation?
An equation that is true for all values of the variable, such as 2(x + 1) = 2x + 2. It results in infinite solutions.
What is a contradiction equation?
An equation that is false for all values, such as x + 1 = x + 2. It results in no solution.
How do I know if my answer is correct?
Take the answer for x, plug it back into the original equation, and verify that both sides equal the same number.
Does the order of a, b, and c matter?
Yes. The equation is strictly structured as ax + b = c. Swapping the values will change the equation and the answer.
Can I solve quadratic equations here?
No. This tool is only for linear equations (degree 1). Quadratic equations have an x^2 term and require a different solver.
What if my equation is in a different format, like b = ax + c?
You will need to rearrange it into the standard ax + b = c format, or manually apply inverse operations, before using the calculator.
Why did my answer come out as a decimal?
If c - b is not perfectly divisible by a, the solution will be a decimal. For example, 3x = 10 results in x = 3.3333.
How precise is the answer?
The result is rounded to 4 decimal places. However, the underlying calculation uses full precision.
Does this tool show the steps?
It shows the final solution and a brief breakdown. For full step-by-step algebra, you would need a dedicated algebra tutor.
Open the calculator All guides