Step by Step Algebra Calculator

Step-by-Step Linear Equation Solver (ax + b = c)

Enter the coefficients and constants for your linear equation in the form ax + b = c to see the step-by-step solution.

Enter values and click "Solve Equation" to see the steps.

function calculateAlgebra() { var a = parseFloat(document.getElementById("coefficientA").value); var b = parseFloat(document.getElementById("constantB").value); var c = parseFloat(document.getElementById("constantC").value); var resultDiv = document.getElementById("result"); var output = ""; // Input validation if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } output += "

Solution Steps:

"; output += "Given equation: " + a + "x + " + b + " = " + c + ""; // Handle a = 0 case if (a === 0) { if (b === c) { output += "Step 1: Subtract " + b + " from both sides: 0x = " + (c - b) + ""; output += "Since 0 = 0, this equation is true for any value of x."; output += "Result: Infinite Solutions"; } else { output += "Step 1: Subtract " + b + " from both sides: 0x = " + (c - b) + ""; output += "Since 0 does not equal " + (c - b) + ", there is no value of x that satisfies the equation."; output += "Result: No Solution"; } } else { // Step 1: Subtract b from both sides var cMinusB = c – b; output += "Step 1: Subtract " + b + " from both sides to isolate the term with x."; output += "" + a + "x + " + b + " - " + b + " = " + c + " - " + b + ""; output += "Simplifies to: " + a + "x = " + cMinusB + ""; // Step 2: Divide by a var x = cMinusB / a; output += "Step 2: Divide both sides by " + a + " to solve for x."; output += "" + a + "x / " + a + " = " + cMinusB + " / " + a + ""; output += "Simplifies to: x = " + x.toFixed(4) + ""; // ToFixed for cleaner output output += "Final Solution: x = " + x.toFixed(4) + ""; } resultDiv.innerHTML = output; }

Understanding and Solving Linear Equations

Algebra is a fundamental branch of mathematics that uses letters (variables) to represent unknown numbers. One of the most common types of equations you'll encounter is a linear equation. A linear equation is an algebraic equation in which each term has an exponent of 1, and when plotted on a graph, it forms a straight line.

What is a Linear Equation?

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

  • x is the variable (the unknown value we want to find).
  • 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 when solving a linear equation is to find the value of x that makes the equation true.

Why Solve Linear Equations?

Linear equations are not just abstract mathematical problems; they have countless real-world applications. They are used in:

  • Finance: Calculating simple interest, budgeting, or determining break-even points.
  • Physics: Describing motion, force, and energy relationships.
  • Engineering: Designing structures, circuits, and systems.
  • Everyday Life: Figuring out how much of an ingredient to use, calculating travel time, or splitting a bill.

How to Solve ax + b = c Step-by-Step

The process of solving a linear equation involves isolating the variable x on one side of the equation. This is done by performing inverse operations to both sides of the equation to maintain balance.

  1. Isolate the term with x: The first step is to get the ax term by itself on one side of the equation. To do this, you perform the inverse operation of what's being done to b. If b is being added, you subtract b from both sides. If b were being subtracted, you would add it.

    Given: ax + b = c

    Subtract b from both sides: ax + b - b = c - b

    Result: ax = c - b

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

    Given: ax = c - b

    Divide by a (assuming a ≠ 0): ax / a = (c - b) / a

    Result: x = (c - b) / a

Special Cases: When a = 0

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

  • Infinite Solutions: If b is equal to c (e.g., 0x + 5 = 5, which simplifies to 5 = 5), then the equation is true for any value of x. There are infinitely many solutions.
  • No Solution: If b is not equal to c (e.g., 0x + 5 = 7, which simplifies to 5 = 7), then the equation is false. There is no value of x that can satisfy the equation.

How to Use the Calculator

Our Step-by-Step Linear Equation Solver makes it easy to understand the solution process:

  1. Input 'a': Enter the coefficient of x.
  2. Input 'b': Enter the constant term on the left side of the equation.
  3. Input 'c': Enter the constant term on the right side of the equation.
  4. Click "Solve Equation": The calculator will display each step taken to solve for x, along with the final solution or an indication of infinite/no solutions.

Example: Solving 3x + 7 = 19

Let's use the calculator to solve the equation 3x + 7 = 19.

  • Coefficient 'a' = 3
  • Constant 'b' = 7
  • Constant 'c' = 19

Here's how the calculator would break it down:

  1. Given Equation: 3x + 7 = 19
  2. Step 1: Subtract 7 from both sides.

    3x + 7 - 7 = 19 - 7

    Simplifies to: 3x = 12

  3. Step 2: Divide both sides by 3.

    3x / 3 = 12 / 3

    Simplifies to: x = 4

Final Solution: x = 4

This calculator is a great tool for students learning algebra or anyone needing a quick, step-by-step solution to linear equations.

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