Linear Equation Solver
Solve linear equations step by step. Enter equations in the form ax + b = c or ax + b = cx + d and get the solution with detailed steps. Perfect for students, teachers, and anyone learning algebra.
What Is a Linear Equation?
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power. Linear equations are called "linear" because their graphs are straight lines.
The general form of a linear equation in one variable is:
ax + b = 0 or ax + b = cx + d
Where:
a, b, c, d are constants (numbers)
x is the variable we want to solve for
Solving a linear equation means finding the value of the variable that makes the equation true. This value is called the solution or root of the equation.
How Does the Linear Equation Solver Work?
The solver follows these steps:
- Step 1: Identify the equation type and arrange terms.
- Step 2: Move all variable terms to one side and constant terms to the other.
- Step 3: Combine like terms.
- Step 4: Divide both sides by the coefficient of the variable.
- Step 5: Verify the solution by substituting it back into the original equation.
For ax + b = c, the solution is: x = (c − b) / a
For ax + b = cx + d, the solution is: x = (d − b) / (a − c)
The calculator displays the solution with step-by-step details and verifies the result by substituting the solution back into the original equation.
Why Use This Linear Equation Solver?
- Two Equation Types: Supports ax + b = c and ax + b = cx + d.
- Step-by-Step Solutions: Learn how to solve equations with detailed steps.
- Visual Verification: Optional graph shows the equation as a line.
- Educational: Perfect for students learning algebra.
- Free & Private: No registration, no data storage.
❓ Linear Equation Solver FAQ
What is a linear equation?
A linear equation is an algebraic equation where each term is either a constant or a constant times a variable raised to the first power. The graph of a linear equation is a straight line.
What is the general form of a linear equation?
The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. This calculator also supports equations with variables on both sides: ax + b = cx + d.
How do I solve a linear equation?
To solve a linear equation: 1) Simplify both sides if needed. 2) Move variable terms to one side and constants to the other. 3) Combine like terms. 4) Divide by the coefficient of the variable. 5) Check your answer by substituting it back into the original equation.
What is the solution to ax + b = c?
The solution is x = (c − b) / a. For example, if 2x + 5 = 13, then x = (13 − 5) / 2 = 4.
What is the solution to ax + b = cx + d?
The solution is x = (d − b) / (a − c). For example, if 3x + 2 = x + 8, then x = (8 − 2) / (3 − 1) = 3.
What is the difference between a linear equation and a quadratic equation?
A linear equation has the variable raised to the first power (ax + b = 0). A quadratic equation has the variable raised to the second power (ax² + bx + c = 0). This solver handles linear equations only.
What if the coefficient of x is zero?
If a = 0 in ax + b = c, then the equation becomes b = c, which is either always true (infinite solutions) or never true (no solution). The calculator handles these special cases.
What is the verification step?
Verification is the process of substituting the solution back into the original equation to confirm that both sides are equal. The calculator shows the verification step for your answer.
Can I solve equations with fractions or decimals?
Yes. The calculator accepts decimal and fractional inputs (as decimals). It will solve the equation and display the solution as a decimal or simplified fraction.
What does the graph show?
The graph displays the equation as a straight line. The x-intercept (where the line crosses the x-axis) is the solution to the equation. This visual representation helps you understand the solution.
What is the difference between a solution and a root?
In the context of equations, "solution" and "root" mean the same thing — the value of the variable that makes the equation true. Both terms are used interchangeably.
How do I check if my solution is correct?
Substitute your solution back into the original equation. If both sides are equal, your solution is correct. The calculator does this verification for you automatically.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations with the same variables. For example, 2x + y = 5 and x − y = 1 is a system of two equations. This solver handles single linear equations only.
What is the slope of a linear equation?
The slope of a linear equation is the coefficient of x when the equation is written in the form y = mx + b. For ax + b = c, the slope is a if written as y = ax + (b − c).
How do I use this calculator for homework?
Enter your equation coefficients and click "Solve Equation." The calculator will show the solution and step-by-step steps (if enabled). Use it to check your work or to understand the solving process.
What if my equation has variables on both sides?
Select the "ax + b = cx + d" mode. Enter the coefficients for both sides, and the calculator will solve the equation with variables on both sides.
What if my equation has parentheses or fractions?
This calculator expects equations in the simplified form ax + b = c or ax + b = cx + d. If your equation has parentheses or fractions, simplify it first before entering the coefficients.
Is this calculator free to use?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.