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Algebra Calculator

Linear Equation Calculator

Solve equations in the form ax + b = c and view every calculation step. Enter the coefficients below to find the value of x instantly.

Solve Your Linear Equation

Enter the values of a, b, and c from the equation ax + b = c.

Equation: 2x + 6 = 14
For an equation such as 3x − 5 = 16, enter a = 3, b = −5, and c = 16.
Solution
x = 4

Step-by-Step Calculation

What Is a Linear Equation Calculator?

A linear equation calculator is an online algebra tool that finds the value of an unknown variable in a first-degree equation. This calculator solves equations written in the standard one-variable form ax + b = c.

Instead of only displaying the final result, the calculator explains how the constant is moved to the other side and how both sides are divided by the coefficient of x. This makes it useful for checking homework and understanding the equation-solving process.

How to Use the Linear Equation Calculator

  1. Identify the values of a, b, and c in your equation.
  2. Enter the coefficient of x in the first field.
  3. Enter the constant from the left side in the second field.
  4. Enter the value from the right side in the third field.
  5. Click the “Solve Equation” button to calculate x.
  6. Review the displayed solution and calculation steps.
Important: Enter negative constants with a minus sign. For example, in 5x − 7 = 18, the value of b is −7.

How the Calculator Solves ax + b = c

The goal is to isolate x on one side of the equation. The calculator uses inverse operations to remove the constant and coefficient.

Step 1: Subtract b from both sides

Starting with ax + b = c, subtract b from the left and right sides:

ax = c − b

Step 2: Divide both sides by a

Divide both sides by the coefficient a, provided that a is not zero:

x = (c − b) ÷ a

Linear Equation Example

Suppose you need to solve the following equation:

4x + 7 = 31

Subtract 7 from both sides:

4x = 31 − 7

4x = 24

Now divide both sides by 4:

x = 24 ÷ 4

x = 6

Special Linear Equation Cases

Condition Meaning Result
a ≠ 0 The equation has a nonzero x coefficient. One unique solution
a = 0 and b = c Both sides are equal without using x. Infinitely many solutions
a = 0 and b ≠ c The equation produces a false statement. No solution

Where Are Linear Equations Used?

Linear equations are used whenever two quantities have a constant relationship. They appear in mathematics, business, science, engineering, finance, and many everyday calculations.

  • Calculating the cost of products with a fixed delivery fee.
  • Finding distance when speed and travel time are known.
  • Estimating earnings based on hourly pay.
  • Calculating temperature and measurement conversions.
  • Finding break-even points in business calculations.
  • Analyzing simple patterns and rates of change.

Frequently Asked Questions

Find clear answers to common questions about solving one-variable linear equations.

A linear equation is an equation in which the highest power of the variable is one. A common one-variable form is ax + b = c.
For an equation written as ax + b = c, the calculator uses x = (c − b) ÷ a, provided that a is not equal to zero.
Yes. The calculator accepts positive numbers, negative numbers, zero, and decimal values for a, b, and c.
When a is zero, the equation does not contain an active x term. It may have no solution or infinitely many solutions, depending on whether b equals c.
This version is designed for one-variable equations in the form ax + b = c. A system of equations calculator is required to solve two equations containing variables such as x and y.
Yes. You can use the calculator to solve as many linear equations as needed without registration.