Equation Calculator with Steps

Linear Equation Solver (ax + b = c)

Understanding and Solving Linear Equations with Steps

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 (usually 'x') 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?

The most common form of a linear equation with one variable is ax + b = c, where:

• x is the variable you want to solve for.
• a is the coefficient of x (a number multiplied by x).
• b is a constant term on the left side of the equation.
• c is a constant term on the right side of the equation.

The goal of solving a linear equation is to isolate the variable x on one side of the equation, determining its value.

How to Solve a Linear Equation (ax + b = c) Step-by-Step

Solving a linear equation involves applying inverse operations to both sides of the equation to maintain balance. Here's the general process:

1. Isolate the term with 'x':

   To get the ax term by itself, you need to eliminate the constant b from the left side. You do this by performing the inverse operation of what's currently being done to b. If b is being added, subtract it from both sides. If it's being subtracted, add it to both sides.

   Example: If you have ax + b = c, subtract b from both sides:

   ax + b - b = c - b

   This simplifies to: ax = c - b

2. Isolate 'x':

   Now that you have ax on one side, you need to get x by itself. Since a is being multiplied by x, the inverse operation is division. Divide both sides of the equation by a.

   Example: From ax = c - b, divide both sides by a:

   ax / a = (c - b) / a

   This simplifies to: x = (c - b) / a

Special Cases: When 'a' is Zero

What happens if the coefficient 'a' is 0? The equation becomes 0x + b = c, which simplifies to b = c.

• If b = c (e.g., 0x + 5 = 5), then the equation is true for any value of x. This means there are infinite solutions.
• If b ≠ c (e.g., 0x + 5 = 7), then the equation is false. This means there is no solution.

Using the Linear Equation Solver

Our calculator simplifies this process for you. Simply input the values for the coefficient 'a', the constant 'b' (from the left side), and the constant 'c' (from the right side) into the respective fields. Click "Solve Equation," and the calculator will instantly display the original equation, each step of the solution process, and the final value of 'x'. This tool is perfect for checking your homework, understanding the mechanics of solving linear equations, or quickly finding solutions for practical problems.

Example Calculation:

Let's solve the equation 3x + 7 = 22 using the calculator's logic:

• Input: a = 3, b = 7, c = 22
• Original Equation: 3x + 7 = 22
• Step 1: Subtract 7 from both sides
  • 3x + 7 – 7 = 22 – 7
  • 3x = 15
• Step 2: Divide both sides by 3
  • 3x / 3 = 15 / 3
  • x = 5
• Final Solution: x = 5

This calculator provides a clear, step-by-step breakdown, making it an excellent resource for learning and verifying solutions to linear equations.