Google Algebra Calculator

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Algebraic Equation Solver (ax + b = c)

function solveEquation() { var a = parseFloat(document.getElementById("coefficientA").value); var b = parseFloat(document.getElementById("constantB").value); var c = parseFloat(document.getElementById("resultC").value); var resultDiv = document.getElementById("equationResult"); if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } var x; if (a === 0) { if (b === c) { resultDiv.innerHTML = "Result: Infinite solutions (any 'x' works)."; } else { resultDiv.innerHTML = "Result: No solution (equation is contradictory)."; } } else { x = (c – b) / a; resultDiv.innerHTML = "Solution for x: " + 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: 500px; margin: 20px auto; border: 1px solid #ddd; } .calculator-container h2 { text-align: center; color: #333; margin-bottom: 20px; font-size: 1.8em; } .calculator-form .form-group { margin-bottom: 15px; } .calculator-form label { display: block; margin-bottom: 5px; color: #555; font-weight: bold; } .calculator-form input[type="number"] { width: calc(100% – 22px); padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1em; } .calculate-button { width: 100%; padding: 12px; background-color: #007bff; color: white; border: none; border-radius: 4px; font-size: 1.1em; cursor: pointer; transition: background-color 0.3s ease; } .calculate-button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding: 15px; background-color: #e9ecef; border-radius: 4px; border: 1px solid #dee2e6; text-align: center; font-size: 1.2em; color: #333; min-height: 50px; display: flex; align-items: center; justify-content: center; } .calculator-result p { margin: 0; font-weight: bold; } .calculator-result .error { color: #dc3545; }

Understanding and Solving Linear Equations with Our Calculator

Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating these symbols. One of the most common tasks in algebra is solving equations, particularly linear equations. A linear equation is an equation for a straight line, meaning it has no exponents higher than one on its variables.

What is a Linear Equation?

A simple linear equation in one variable, typically 'x', can be expressed in the standard form: ax + b = c. In this equation:

  • 'a' is the coefficient of 'x'. It's the number that multiplies the variable 'x'.
  • 'x' is the variable we want to solve for.
  • 'b' is a constant term, a number added or subtracted.
  • 'c' is another constant term, representing the result of the expression ax + b.

The goal is to find the value of 'x' that makes the equation true.

How to Solve ax + b = c Manually

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

  1. Subtract 'b' from both sides: This cancels out 'b' on the left side, leaving ax = c - b.
  2. Divide both sides by 'a': This cancels out 'a' on the left side, leaving x = (c - b) / a.

This formula provides the solution for 'x', provided that 'a' is not zero.

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, if you have 0x + 5 = 5, this simplifies to 5 = 5. This statement is always true, regardless of the value of 'x'. Therefore, there are infinite solutions. Any real number for 'x' will satisfy the equation.
  • If b ≠ c: For example, if you have 0x + 5 = 10, this simplifies to 5 = 10. This statement is false. No value of 'x' can make this equation true. Therefore, there is no solution.

Using Our Algebraic Equation Solver

Our calculator simplifies the process of solving linear equations of the form ax + b = c. Simply input the values for 'a', 'b', and 'c' into the respective fields, and the calculator will instantly provide the solution for 'x', or indicate if there are infinite or no solutions.

Examples of Linear Equations:

Let's look at a few examples to illustrate how the calculator works:

Example 1: Standard Solution

  • Equation: 2x + 5 = 15
  • Inputs:
    • Coefficient 'a' = 2
    • Constant 'b' = 5
    • Result 'c' = 15
  • Calculation: x = (15 - 5) / 2 = 10 / 2 = 5
  • Calculator Output: Solution for x: 5.0000

Example 2: Negative Numbers

  • Equation: -3x + 7 = -8
  • Inputs:
    • Coefficient 'a' = -3
    • Constant 'b' = 7
    • Result 'c' = -8
  • Calculation: x = (-8 - 7) / -3 = -15 / -3 = 5
  • Calculator Output: Solution for x: 5.0000

Example 3: Infinite Solutions

  • Equation: 0x + 10 = 10
  • Inputs:
    • Coefficient 'a' = 0
    • Constant 'b' = 10
    • Result 'c' = 10
  • Calculation: Since 'a' is 0 and 'b' equals 'c', there are infinite solutions.
  • Calculator Output: Infinite solutions (any 'x' works).

Example 4: No Solution

  • Equation: 0x + 4 = 9
  • Inputs:
    • Coefficient 'a' = 0
    • Constant 'b' = 4
    • Result 'c' = 9
  • Calculation: Since 'a' is 0 and 'b' does not equal 'c', there is no solution.
  • Calculator Output: No solution (equation is contradictory).

This tool is perfect for students, educators, or anyone needing to quickly solve linear equations without manual calculation, helping to verify answers or understand the underlying algebraic principles.

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