Step by Step Algebra Calculator

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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, which means finding the value(s) of a variable that make the equation true. This calculator focuses on solving a simple linear equation of the form ax + b = c, where 'x' is the unknown variable, and 'a', 'b', and 'c' are known numbers.

Understanding Linear Equations

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 general form we're tackling here is ax + b = c:

  • a: This is the coefficient of the variable 'x'. It's the number that 'x' is multiplied by.
  • x: This is the variable we want to solve for.
  • b: This is a constant term on the left side of the equation.
  • c: This is a constant term on the right side of the equation.

The goal is to isolate 'x' on one side of the equation, meaning we want to get 'x' by itself.

How to Solve ax + b = c Step-by-Step

To solve for 'x', we use inverse operations to move terms around the equals sign. Remember, whatever you do to one side of the equation, you must do to the other side to maintain equality.

Step 1: Isolate the term with 'x'

The first step is to get the ax term by itself. To do this, we need to eliminate the constant 'b' from the left side. Since 'b' is being added, we perform the inverse operation: subtraction. We subtract 'b' from both sides of the equation:

ax + b - b = c - b

This simplifies to:

ax = c - b

Step 2: Isolate 'x'

Now that we have ax on one side, we need to get 'x' by itself. Since 'a' is multiplying 'x', we perform the inverse operation: division. We divide both sides of the equation by 'a':

ax / a = (c - b) / a

This simplifies to:

x = (c - b) / a

This final formula gives us the value of 'x'.

Using the Linear Equation Solver

Enter the values for 'a', 'b', and 'c' into the calculator below. The calculator will then show you the step-by-step process to find the value of 'x'.

Linear Equation Solver (ax + b = c)

Enter the coefficients and constants for your equation:







function calculateLinearEquation() { var a = parseFloat(document.getElementById('coeffA').value); var b = parseFloat(document.getElementById('constB').value); var c = parseFloat(document.getElementById('constC').value); var resultDiv = document.getElementById('result'); var steps = []; // Input validation if (isNaN(a) || isNaN(b) || isNaN(c)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } steps.push("

Solving: " + a + "x + " + b + " = " + c + "

"); // Step 1: Subtract 'b' from both sides steps.push("Step 1: Isolate the 'x' term. Subtract " + b + " from both sides of the equation."); steps.push("" + a + "x + " + b + " – " + b + " = " + c + " – " + b + ""); var cMinusB = c – b; steps.push("" + a + "x = " + cMinusB + ""); // Step 2: Divide by 'a' if (a === 0) { if (cMinusB === 0) { steps.push("Result: This equation simplifies to 0x = 0, which means 'x' can be any real number (infinite solutions)."); } else { steps.push("Result: This equation simplifies to 0x = " + cMinusB + ", which has no solution."); } } else { steps.push("Step 2: Isolate 'x'. Divide both sides by " + a + "."); steps.push("" + a + "x / " + a + " = " + cMinusB + " / " + a + ""); var x = cMinusB / a; steps.push("x = " + x.toFixed(4) + ""); // Display x to 4 decimal places steps.push("Final Solution: x = " + x.toFixed(4) + ""); } resultDiv.innerHTML = steps.join("); }

Example Calculation

Let's solve the equation 2x + 5 = 15 using the steps outlined above:

  1. Identify a, b, c: Here, a = 2, b = 5, and c = 15.
  2. Step 1: Subtract 'b' from both sides.

    2x + 5 - 5 = 15 - 5

    2x = 10

  3. Step 2: Divide by 'a'.

    2x / 2 = 10 / 2

    x = 5

So, the solution to 2x + 5 = 15 is x = 5.

Why is this important?

Solving linear equations is a foundational skill in algebra and is used extensively in various fields, including:

  • Science: Calculating unknown variables in physics formulas (e.g., force, velocity, acceleration).
  • Engineering: Designing structures, circuits, and systems where relationships between quantities are linear.
  • Economics: Modeling supply and demand, cost analysis, and financial projections.
  • Computer Science: Developing algorithms and understanding computational complexity.

Mastering these basic algebraic manipulations is crucial for tackling more complex mathematical problems.

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