Linear Equation Calculator

Linear Equation Solver (Ax + B = C)

Understanding and Solving Linear Equations with Our Calculator

A linear equation is a fundamental concept in algebra, representing a straight line when graphed. It's an equation where the highest power of the variable is 1. These equations are widely used in various fields, from physics and engineering to economics and everyday problem-solving.

What is a Linear Equation?

In its simplest form, a linear equation with one variable can be written as:

Ax + B = C

• A is the coefficient of the variable x. It's a number that multiplies x.
• x is the variable you are trying to solve for.
• B is a constant term, a number added or subtracted.
• C is the result of the equation, another constant.

The goal when solving a linear equation is to find the value of x that makes the equation true.

How to Solve Ax + B = C

To solve for x, we use basic algebraic operations to isolate x on one side of the equation:

1. Subtract B from both sides:
   Ax + B - B = C - B
Ax = C - B
2. Divide both sides by A:
   x = (C - B) / A

This formula allows us to directly calculate the value of x once A, B, and C are known.

Edge Cases: When A = 0

Special situations arise when the coefficient A is zero:

• If A = 0 and C – B = 0 (i.e., 0 = 0): This means the equation simplifies to 0 = 0. In this case, any value of x will satisfy the equation, leading to infinite solutions.
• If A = 0 and C – B ≠ 0 (i.e., 0 = a non-zero number): This means the equation simplifies to a false statement, such as 0 = 5. In this case, there is no solution for x.

Using Our Linear Equation Calculator

Our calculator simplifies the process of solving linear equations of the form Ax + B = C. Simply input the values for Coefficient A, Constant B, and Equation Result C, and the calculator will instantly provide the value of x.

Examples:

Example 1: Standard Case

• Equation: 2x + 4 = 10
• Coefficient A: 2
• Constant B: 4
• Equation Result C: 10
• Calculation: x = (10 - 4) / 2 = 6 / 2 = 3
• Calculator Output: x = 3

Example 2: Negative Numbers

• Equation: -3x + 5 = -7
• Coefficient A: -3
• Constant B: 5
• Equation Result C: -7
• Calculation: x = (-7 - 5) / -3 = -12 / -3 = 4
• Calculator Output: x = 4

Example 3: Infinite Solutions

• Equation: 0x + 5 = 5
• Coefficient A: 0
• Constant B: 5
• Equation Result C: 5
• Calculator Output: Infinite solutions (0 = 0)

Example 4: No Solution

• Equation: 0x + 5 = 10
• Coefficient A: 0
• Constant B: 5
• Equation Result C: 10
• Calculator Output: No solution (0 = 5, which is false)

This tool is perfect for students learning algebra, educators demonstrating concepts, or anyone needing a quick solution to a linear equation.