Algebra Calculator with Steps Online

Linear Equation Solver: ax + b = c

Result:

Steps:

function calculateLinearEquation() { var a = parseFloat(document.getElementById("coefficientA").value); var b = parseFloat(document.getElementById("constantB").value); var c = parseFloat(document.getElementById("constantC").value); var solutionOutput = document.getElementById("solutionOutput"); var stepsOutput = document.getElementById("stepsOutput"); solutionOutput.innerHTML = ""; stepsOutput.innerHTML = ""; if (isNaN(a) || isNaN(b) || isNaN(c)) { solutionOutput.innerHTML = "Please enter valid numbers for all fields."; return; } var steps = []; steps.push("Given equation: " + a + "x + " + b + " = " + c); if (a === 0) { if (c – b === 0) { solutionOutput.innerHTML = "Infinite solutions (0x = 0)"; steps.push("Subtract " + b + " from both sides: 0x = " + (c – b)); steps.push("Since 0 = 0, any real number for x satisfies the equation."); } else { solutionOutput.innerHTML = "No solution (0x = " + (c – b) + ")"; steps.push("Subtract " + b + " from both sides: 0x = " + (c – b)); steps.push("Since 0 does not equal " + (c – b) + ", there is no solution."); } } else { // Step 1: Isolate the 'ax' term var cMinusB = c – b; steps.push("Subtract " + b + " from both sides:"); steps.push(a + "x = " + c + " – " + b); steps.push(a + "x = " + cMinusB); // Step 2: Solve for 'x' var x = cMinusB / a; steps.push("Divide both sides by " + a + ":"); steps.push("x = " + cMinusB + " / " + a); steps.push("x = " + x); solutionOutput.innerHTML = "The solution is x = " + x; } stepsOutput.innerHTML = steps.join("\n"); }

Understanding Linear Equations and How to Solve Them

A linear equation is a fundamental concept in algebra, representing a straight line when graphed. It's an equation where the highest power of the variable (usually 'x') is 1. The most common form of a linear equation with one variable is ax + b = c, where:

  • a is the coefficient of the variable x.
  • x is the variable we want to solve for.
  • b is a constant term.
  • c is another constant term.

The Goal of Solving a Linear Equation

The primary goal when solving a linear equation is to isolate the variable x on one side of the equation. This means performing inverse operations to move all other terms to the opposite side.

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

  1. Isolate the term with 'x': To get the ax term by itself, you need to eliminate the constant b from the left side. You do this by performing the inverse operation of what's currently happening to b. If b is being added, you subtract b from both sides of the equation. If b were being subtracted, you would add it.
    ax + b - b = c - b
    ax = c - b
  2. Solve for 'x': Now that you have ax on one side, you need to get x by itself. Since a is multiplying x, the inverse operation is division. Divide both sides of the equation by a.
    ax / a = (c - b) / a
    x = (c - b) / a

Important Considerations (Edge Cases)

  • If a = 0:
    • If the equation becomes 0x = 0 (meaning c - b = 0), then any real number for x will satisfy the equation. This means there are infinite solutions.
    • If the equation becomes 0x = (a non-zero number) (meaning c - b ≠ 0), then there is no value of x that can make this true. In this case, there is no solution.

How to Use the Calculator

Our Linear Equation Solver simplifies this process for you. Simply input the values for the coefficient 'a', constant 'b', and constant 'c' from your equation ax + b = c into the respective fields. Click "Solve Equation," and the calculator will instantly display the value of 'x' along with a detailed breakdown of each step taken to reach the solution, including handling the special cases where 'a' might be zero.

This tool is perfect for students learning algebra, or anyone needing a quick and accurate solution to a linear equation.

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