Algebra Calculator and Steps

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Linear Equation Solver: ax + b = c

Result:

Enter values and click 'Solve Equation'

Steps:

Steps will appear here.

function calculateLinearEquation() { var a = parseFloat(document.getElementById("coefficientA").value); var b = parseFloat(document.getElementById("constantB").value); var c = parseFloat(document.getElementById("constantC").value); var resultX = document.getElementById("resultX"); var stepsOutput = document.getElementById("stepsOutput"); if (isNaN(a) || isNaN(b) || isNaN(c)) { resultX.innerHTML = "Please enter valid numbers for all fields."; stepsOutput.innerHTML = "

Steps:

Invalid input detected."; return; } var stepsHtml = "

Steps:

"; stepsHtml += "Given equation: " + a + "x + " + b + " = " + c + ""; if (a === 0) { if (b === c) { resultX.innerHTML = "Result: Infinite Solutions"; stepsHtml += "If a = 0, the equation becomes " + b + " = " + c + "."; stepsHtml += "Since " + b + " equals " + c + ", this statement is always true, meaning there are infinite solutions for x."; } else { resultX.innerHTML = "Result: No Solution"; stepsHtml += "If a = 0, the equation becomes " + b + " = " + c + "."; stepsHtml += "Since " + b + " does not equal " + c + ", this statement is false, meaning there is no solution for x."; } } else { // Step 1: Subtract b from both sides var cMinusB = c – b; stepsHtml += "Step 1: Isolate the 'ax' term. Subtract " + b + " from both sides of the equation."; stepsHtml += "" + a + "x + " + b + " - " + b + " = " + c + " - " + b + ""; stepsHtml += "" + a + "x = " + cMinusB + ""; // Step 2: Divide by a var xValue = cMinusB / a; stepsHtml += "Step 2: Solve for 'x'. Divide both sides by " + a + " (the coefficient of x)."; stepsHtml += "" + a + "x / " + a + " = " + cMinusB + " / " + a + ""; stepsHtml += "x = " + xValue.toFixed(4) + ""; resultX.innerHTML = "Result: x = " + xValue.toFixed(4) + ""; } stepsOutput.innerHTML = stepsHtml; }

Understanding and Solving Linear Equations

Algebra is a fundamental branch of mathematics that uses letters (variables) to represent unknown numbers in equations. One of the most common types of equations you'll encounter is the 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. The simplest form of a linear equation with one variable is often written as ax + b = c.

What is a Linear Equation?

In the equation ax + b = c:

  • x is the variable (the unknown value we want to find).
  • a is the coefficient of x. It's a number that multiplies 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.

How to Solve a Linear Equation Manually

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, maintaining balance. Here are the general steps:

  1. Isolate the term with x: Add or subtract the constant term (b) from both sides of the equation. This moves all constant terms to one side and leaves the ax term on the other.
    ax + b - b = c - b
    ax = c - b
  2. Solve for x: Divide both sides of the equation by the coefficient of x (a). This will give you the value of x.
    ax / a = (c - b) / a
    x = (c - b) / a

Example: Step-by-Step Solution

Let's solve the equation 3x + 5 = 14 using the manual steps:

  1. Given Equation: 3x + 5 = 14
  2. Step 1: Subtract 5 from both sides.
    3x + 5 - 5 = 14 - 5
    3x = 9
  3. Step 2: Divide both sides by 3.
    3x / 3 = 9 / 3
    x = 3

So, the solution to the equation 3x + 5 = 14 is x = 3.

Using the Linear Equation Solver

Our calculator above simplifies this process. Simply input 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 provide the value of 'x' along with a detailed breakdown of each step, just like you would solve it manually. This tool is perfect for checking your homework, understanding the process, or quickly solving equations.

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