Step by Step Calculator

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

Solution:

Enter values and click "Solve Equation" to see the step-by-step solution.

function calculateLinearEquation() { 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 steps = "; if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = '

Error:

Please enter valid numbers for all fields.'; return; } steps += '

Step-by-Step Solution:

'; steps += 'We are solving the linear equation in the form: ax + b = c'; steps += 'Given values: a = ' + a + ', b = ' + b + ', c = ' + c + ''; steps += 'The equation becomes: ' + a + 'x + ' + b + ' = ' + c + ''; if (a === 0) { var rightSide = c – b; if (rightSide === 0) { steps += 'Step 1: Subtract ' + b + ' from both sides:'; steps += " + a + 'x + ' + b + ' – ' + b + ' = ' + c + ' – ' + b + "; steps += 'This simplifies to: 0x = 0'; steps += 'Result: This equation has infinitely many solutions, as any value of x satisfies 0 = 0.'; } else { steps += 'Step 1: Subtract ' + b + ' from both sides:'; steps += " + a + 'x + ' + b + ' – ' + b + ' = ' + c + ' – ' + b + "; steps += 'This simplifies to: 0x = ' + rightSide + ''; steps += 'Result: This equation has no solution, as 0 cannot equal ' + rightSide + '.'; } } else { // Step 1: Subtract 'b' from both sides steps += 'Step 1: Isolate the term with x (ax)'; steps += 'Subtract ' + b + ' from both sides of the equation:'; steps += " + a + 'x + ' + b + ' – ' + b + ' = ' + c + ' – ' + b + "; var cMinusB = c – b; steps += 'This simplifies to: ' + a + 'x = ' + cMinusB + ''; // Step 2: Divide by 'a' steps += 'Step 2: Solve for x'; steps += 'Divide both sides by the coefficient ' + a + ':'; steps += " + a + 'x / ' + a + ' = ' + cMinusB + ' / ' + a + "; var x = cMinusB / a; steps += 'This simplifies to: x = ' + x.toFixed(4) + ''; // Display with 4 decimal places steps += 'Final Solution: x = ' + x.toFixed(4) + "; } resultDiv.innerHTML = steps; }

Understanding the Step-by-Step Linear Equation Solver

A linear equation is a fundamental concept in algebra, representing a straight line when graphed. It's an equation that can be written in the form ax + b = c, where 'x' is the variable, and 'a', 'b', and 'c' are constants. Solving a linear equation means finding the value of 'x' that makes the equation true.

Why Solve Linear Equations?

Linear equations are not just abstract mathematical problems; they are used to model and solve real-world situations across various fields:

  • Science: Calculating speed, distance, time, or concentrations in chemistry.
  • Engineering: Designing structures, analyzing circuits, or predicting system behavior.
  • Economics: Modeling supply and demand, calculating costs, or predicting market trends.
  • Everyday Life: Budgeting, calculating tips, or figuring out how much of an ingredient to use.

How This Calculator Works

Our Step-by-Step Linear Equation Solver takes the coefficients and constants you provide for the equation ax + b = c and walks you through the algebraic steps to find the value of 'x'. Here's the general process:

  1. Identify 'a', 'b', and 'c': The calculator first identifies the numerical values you've entered for the coefficient of 'x' (a), the constant term on the left side (b), and the constant term on the right side (c).
  2. Isolate the 'ax' term: The goal is to get the term containing 'x' by itself on one side of the equation. This is achieved by performing the inverse operation of addition or subtraction. If 'b' is added, we subtract 'b' from both sides of the equation. This maintains the equality.
  3. Solve for 'x': Once 'ax' is isolated, the next step is to get 'x' by itself. Since 'a' is multiplied by 'x', we perform the inverse operation: division. We divide both sides of the equation by 'a'. This gives us the value of 'x'.
  4. Handle Special Cases:
    • If 'a' is 0 and (c – b) is also 0 (e.g., 0x = 0), then any value of 'x' will satisfy the equation, meaning there are infinitely many solutions.
    • If 'a' is 0 but (c – b) is not 0 (e.g., 0x = 5), then there is no value of 'x' that can satisfy the equation, meaning there is no solution.

Example Calculation

Let's use the default values in the calculator: a = 2, b = 5, c = 15.

The equation is: 2x + 5 = 15

  1. Original Equation: 2x + 5 = 15
  2. Step 1: Subtract 5 from both sides
    2x + 5 – 5 = 15 – 5
    2x = 10
  3. Step 2: Divide both sides by 2
    2x / 2 = 10 / 2
    x = 5

Thus, the solution is x = 5. You can verify this by plugging 5 back into the original equation: 2(5) + 5 = 10 + 5 = 15, which is correct.

Use this calculator to practice solving linear equations and understand each step involved in reaching the solution.

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