Algebra Online Calculator Step for Step

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Algebra Step-by-Step Solver

Solve linear equations of the form: ax + b = c

x +
=

Step-by-Step Solution:

function solveAlgebraStepByStep() { var a = parseFloat(document.getElementById('coeffA').value); var b = parseFloat(document.getElementById('constB').value); var c = parseFloat(document.getElementById('resultC').value); var resultDiv = document.getElementById('algebraResult'); var stepDiv = document.getElementById('stepDetails'); if (isNaN(a) || isNaN(b) || isNaN(c)) { alert('Please enter valid numbers for a, b, and c.'); return; } if (a === 0) { stepDiv.innerHTML = "Error: The coefficient 'a' cannot be zero. If a is 0, then the equation is " + b + " = " + c + ", which is not a linear algebraic equation for x."; resultDiv.style.display = 'block'; return; } var steps = ""; steps += "Equation: " + a + "x + " + b + " = " + c + ""; // Step 1: Subtract b var step1Result = c – b; steps += "Step 1: Subtract " + b + " from both sides to isolate the term with x."; steps += " " + a + "x = " + c + " – (" + b + ")"; steps += " " + a + "x = " + step1Result + ""; // Step 2: Divide by a var finalX = step1Result / a; steps += "Step 2: Divide both sides by " + a + " to solve for x."; steps += " x = " + step1Result + " / " + a + ""; steps += " x = " + finalX.toFixed(4).replace(/\.?0+$/, "") + ""; // Final verification steps += "Verification:"; steps += " " + a + "(" + finalX.toFixed(4).replace(/\.?0+$/, "") + ") + " + b + " = " + (a * finalX + b) + " (Correct!)"; stepDiv.innerHTML = steps; resultDiv.style.display = 'block'; }

Understanding Linear Equations: The Algebra Online Calculator

Algebra is the branch of mathematics that uses letters and symbols to represent numbers in equations and formulas. For many students, solving for "x" can feel like a mystery. Our algebra online calculator step for step is designed to demystify the process by breaking down the logic used to isolate variables.

What is a Linear Equation?

A linear equation is an algebraic equation where the highest power of the variable (usually x) is one. The most common form is ax + b = c, where:

  • a is the coefficient (the number multiplying the variable).
  • x is the unknown variable we are trying to find.
  • b and c are constants (fixed numbers).

The "Golden Rule" of Algebra

The most important rule in algebra is: Whatever you do to one side of the equation, you must do to the other. This keeps the equation balanced. To solve for x, we use "inverse operations" to peel away the numbers surrounding it.

Example Calculation

Let's say you have the equation: 4x + 12 = 36.

  1. Step 1: Isolate the variable term. We see a +12 on the left. The inverse of addition is subtraction. We subtract 12 from both sides.
    4x = 36 – 12
    4x = 24
  2. Step 2: Solve for x. Now x is multiplied by 4. The inverse of multiplication is division. We divide both sides by 4.
    x = 24 / 4
    x = 6

Why Use a Step-by-Step Calculator?

While getting the final answer is important, understanding the how is what builds mathematical fluency. Using an algebra online calculator with steps helps students verify their homework, recognize patterns in problem-solving, and gain confidence in their ability to manipulate equations manually.

Operation Inverse Operation
Addition (+) Subtraction (-)
Multiplication (×) Division (÷)
Square (x²) Square Root (√)

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