Step by Step Math Calculator Free

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

Enter the coefficients for the linear equation in the form ax + b = c.

.calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, 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-form .form-group { margin-bottom: 15px; display: flex; flex-direction: column; } .calculator-form label { margin-bottom: 5px; color: #555; font-weight: bold; } .calculator-form 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: 4px; cursor: pointer; font-size: 1.1em; width: 100%; box-sizing: border-box; transition: background-color 0.3s ease; } .calculate-button:hover { background-color: #0056b3; } .calculator-result { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 8px; color: #155724; font-size: 1.1em; line-height: 1.6; } .calculator-result h3 { color: #0f5132; margin-top: 0; font-size: 1.4em; } .calculator-result p { margin-bottom: 8px; } .calculator-result strong { color: #0f5132; } .calculator-result ul { list-style-type: decimal; padding-left: 20px; margin-top: 10px; } .calculator-result ul li { margin-bottom: 5px; } .error-message { color: #dc3545; background-color: #f8d7da; border-color: #f5c6cb; padding: 10px; border-radius: 4px; margin-top: 15px; } 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 output = "; if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = '

Please enter valid numbers for all fields.

'; return; } output += '

Step-by-Step Solution:

'; output += 'Given the linear equation in the form ax + b = c:'; output += '' + a + 'x + ' + b + ' = ' + c + ''; output += '

'; // Step 1: Isolate the term with x output += '
• Step 1: Subtract ' + b + ' from both sides of the equation.
'; var cMinusB = c – b; output += '
• ' + a + 'x = ' + c + ' - ' + b + '
'; output += '
• Simplify: ' + a + 'x = ' + cMinusB + '
'; // Step 2: Solve for x if (a === 0) { if (cMinusB === 0) { output += '
• Step 2: Divide both sides by ' + a + '.
'; output += '
• Since the coefficient of x (a) is 0 and the right side is also 0 (0x = 0), this equation has infinitely many solutions. Any real number for x will satisfy the equation.
'; output += '

'; output += 'Final Solution: Infinitely many solutions.'; } else { output += '

Step 2: Divide both sides by ' + a + '.

'; output += '

Since the coefficient of x (a) is 0 and the right side is not 0 (0x = ' + cMinusB + '), this equation has no solution. There is no value of x that can satisfy this equation.

'; output += ''; output += 'Final Solution: No solution.'; } } else { output += '

Step 2: Divide both sides by ' + a + '.

'; var x = cMinusB / a; output += '

x = ' + cMinusB + ' / ' + a + '

'; output += '

Simplify: x = ' + x + '

'; output += ''; output += 'Final Solution: x = ' + x + ''; } resultDiv.innerHTML = output; }

A "step-by-step math calculator" is a powerful tool designed to not only provide the answer to a mathematical problem but also to illustrate the detailed process of arriving at that solution. This particular calculator focuses on solving linear equations of the form ax + b = c, which are fundamental in algebra and various scientific disciplines. Understanding the steps involved in solving such equations is crucial for building a strong mathematical foundation.

What is a Linear Equation?

A linear equation is an algebraic equation in which each term has an exponent of 1, and the graph of the equation is a straight line. The most common form for a single-variable linear equation is ax + b = c, where:

• x is the variable (the unknown value we want to find).
• 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.

The goal when solving a linear equation is to isolate the variable x on one side of the equation.

How to Solve a Linear Equation (ax + b = c) Step-by-Step

Solving a linear equation involves applying inverse operations to both sides of the equation to maintain balance and isolate the variable. Here are the general steps:

1. Isolate the term with the variable (ax): To do this, you need to move the constant term b from the left side to the right side. Since b is being added on the left, you perform the inverse operation: subtract b from both sides of the equation.
   ax + b - b = c - b
ax = c - b
2. Solve for the variable (x): Now that you have ax on one side, you need to get x by itself. Since a is being multiplied by x, you perform the inverse operation: divide both sides of the equation by a.
   ax / a = (c - b) / a
x = (c - b) / a

Special Cases:

• If a = 0 and c - b = 0 (e.g., 0x + 5 = 5): The equation simplifies to 0x = 0. This means any value of x will satisfy the equation, leading to infinitely many solutions.
• If a = 0 and c - b ≠ 0 (e.g., 0x + 5 = 7): The equation simplifies to 0x = (non-zero number). This is a contradiction (0 cannot equal a non-zero number), meaning there is no solution for x.

Example Using the Calculator:

Let's solve the equation 3x + 7 = 19 using the calculator.

Here, a = 3, b = 7, and c = 19.

1. Input:
   • Coefficient of x (a): 3
   • Constant term on left (b): 7
   • Constant term on right (c): 19
2. Click "Solve Equation".
3. Output (Step-by-Step):
   • Given equation: 3x + 7 = 19
   • Step 1: Subtract 7 from both sides of the equation.
   • 3x = 19 - 7
   • Simplify: 3x = 12
   • Step 2: Divide both sides by 3.
   • x = 12 / 3
   • Simplify: x = 4

The final solution is x = 4. This calculator helps you visualize each operation, making complex problems easier to understand and learn from.