Calculator Algebra App

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Algebra Equation Solver: ax + b = c

Result:

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("algebraResult"); if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (a === 0) { if (b === c) { resultDiv.innerHTML = "Infinite Solutions (Any value of x satisfies the equation)"; } else { resultDiv.innerHTML = "No Solution (The equation is contradictory)"; } } else { var x = (c – b) / a; resultDiv.innerHTML = "The value of x is: " + x.toFixed(4) + ""; } } .calculator-container { font-family: 'Arial', sans-serif; background-color: #f9f9f9; padding: 20px; border-radius: 8px; box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1); max-width: 600px; margin: 20px auto; border: 1px solid #ddd; } .calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; font-size: 1.8em; } .calculator-content { display: flex; flex-direction: column; gap: 15px; } .input-group { display: flex; flex-direction: column; margin-bottom: 10px; } .input-group label { margin-bottom: 5px; color: #555; font-size: 1em; } .input-group input[type="number"] { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1em; width: 100%; box-sizing: border-box; } .calculate-button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 5px; cursor: pointer; font-size: 1.1em; margin-top: 10px; transition: background-color 0.3s ease; } .calculate-button:hover { background-color: #0056b3; } .result-area { margin-top: 20px; padding: 15px; background-color: #e9ecef; border-radius: 5px; border: 1px solid #dee2e6; } .result-area h3 { color: #333; margin-top: 0; margin-bottom: 10px; font-size: 1.2em; } .calculator-result { font-size: 1.4em; color: #28a745; font-weight: bold; text-align: center; } .calculator-result strong { color: #0056b3; }

Understanding and Solving Linear Equations with Our Algebra App

Algebra is a fundamental branch of mathematics that uses letters (variables) to represent unknown numbers. One of the most common tasks in algebra is solving equations to find the value of these unknown variables. Our Algebra Equation Solver is designed to help you quickly and accurately solve simple linear equations in the standard form: ax + b = c.

What is a Linear Equation?

A linear equation is an algebraic equation in which each term has an exponent of 1, and when graphed, it forms a straight line. The general form we're focusing on 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.

For example, 2x + 5 = 15 is a linear equation where a=2, b=5, and c=15.

How to Solve for 'x' Manually

To solve for x in the equation ax + b = c, you typically follow these steps:

  1. Isolate the term with 'x': Subtract b from both sides of the equation.
    ax + b - b = c - b
    ax = c - b
  2. Solve for 'x': Divide both sides by a (assuming a is not zero).
    ax / a = (c - b) / a
    x = (c - b) / a

Example:

Let's solve 2x + 5 = 15:

  1. Subtract 5 from both sides:
    2x + 5 - 5 = 15 - 5
    2x = 10
  2. Divide both sides by 2:
    2x / 2 = 10 / 2
    x = 5

So, the solution is x = 5.

Special Cases: When 'a' is Zero

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

  • If b = c: For example, 0x + 7 = 7. This simplifies to 7 = 7, which is always true. In this case, any value of x will satisfy the equation, meaning there are infinite solutions.
  • If b ≠ c: For example, 0x + 7 = 10. This simplifies to 7 = 10, which is false. No value of x can make this equation true, so there is no solution.

How to Use the Algebra Equation Solver

Our calculator simplifies this process for you:

  1. Enter Coefficient 'a': Input the number that multiplies x.
  2. Enter Constant 'b': Input the constant term on the left side of the equation.
  3. Enter Constant 'c': Input the constant term on the right side of the equation.
  4. Click "Solve for x": The calculator will instantly display the value of x, or indicate if there are infinite solutions or no solution.

This tool is perfect for students checking their homework, or anyone needing a quick solution to a linear equation. Give it a try with your own numbers!

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