Enter your equation in the form Ax + B = C or Ax = B.
Your solution will appear here.
Understanding and Solving Linear Equations
Linear equations are fundamental in mathematics, forming the basis for many more complex concepts. A linear equation in one variable, typically 'x', is an equation that can be written in the form Ax + B = C, where A, B, and C are constants, and A is non-zero. Our goal when solving such an equation is to find the value of 'x' that makes the equation true.
Types of Linear Equations Handled:
Standard Form: Ax + B = C: This is the most common form. Examples include 5x + 10 = 20.
Simplified Form: Ax = B: This is a special case where B (in the Ax + B = C form) is zero. For instance, 3x = 15.
How to Solve Step-by-Step:
The process involves isolating the variable 'x' on one side of the equation. Here's a breakdown of the algebraic steps:
Combine Like Terms (if necessary): Ensure constants are on one side and terms with 'x' are on the other.
Isolate the 'Ax' term: To do this in the form Ax + B = C, subtract B from both sides of the equation:
Ax + B – B = C – B Ax = C – B
Solve for 'x': Divide both sides by the coefficient A:
Ax / A = (C – B) / A x = (C – B) / A
For the simplified form Ax = B, the process is just step 3: Divide both sides by A.
Calculator Logic:
This calculator simplifies the process. You input the values for A, B, and C based on your equation. If your equation is in the form Ax = B, you can enter 0 for the 'Constant B' field. The calculator then applies the formula x = (C – B) / A to find the solution for 'x'.
Use Cases:
Linear equations and their solutions appear in numerous fields:
Physics: Calculating quantities like velocity, time, or distance when relationships are linear (e.g., distance = speed × time).
Finance: Simple interest calculations, budgeting, or determining break-even points.
Engineering: Modeling physical systems where relationships are often approximated as linear.
Everyday Problems: Pro-rating costs, calculating required ingredients in recipes, or figuring out travel times.
Mastering the ability to solve these basic algebraic equations is a crucial skill for anyone pursuing studies or careers in STEM fields, and it's also incredibly useful for practical, real-world problem-solving.
function solveEquation() {
var a = parseFloat(document.getElementById("coefficientA").value);
var b = parseFloat(document.getElementById("constantB").value);
var c = parseFloat(document.getElementById("resultC").value);
var resultDiv = document.getElementById("result");
resultDiv.textContent = ""; // Clear previous result
// Input validation
if (isNaN(a) || isNaN(c)) {
resultDiv.textContent = "Please enter valid numbers for A and C.";
resultDiv.style.backgroundColor = "#f8d7da";
resultDiv.style.borderColor = "#f5c6cb";
resultDiv.style.color = "#721c24";
return;
}
// If only Ax = B is provided (C is not specified by user, so it's NaN)
// or if the user intends B to be 0 in Ax + B = C
var effectiveC = isNaN(c) ? b : c; // If C is NaN, we assume the input is Ax = B, so C should be the value of B. Otherwise use the provided C.
var effectiveB = isNaN(c) ? 0 : b; // If C is NaN, the B term in Ax + B = C is effectively 0.
// Handle the case where A is zero
if (a === 0) {
if (effectiveC === effectiveB) {
resultDiv.textContent = "Infinite solutions (0 = 0)";
resultDiv.style.backgroundColor = "#d4edda";
resultDiv.style.borderColor = "#c3e6cb";
resultDiv.style.color = "#155724";
} else {
resultDiv.textContent = "No solution (" + effectiveB + " != " + effectiveC + ")";
resultDiv.style.backgroundColor = "#f8d7da";
resultDiv.style.borderColor = "#f5c6cb";
resultDiv.style.color = "#721c24";
}
return;
}
// Calculate the solution
var x = (effectiveC – effectiveB) / a;
// Display the result
if (isNaN(x)) {
resultDiv.textContent = "Calculation error. Please check your inputs.";
resultDiv.style.backgroundColor = "#f8d7da";
resultDiv.style.borderColor = "#f5c6cb";
resultDiv.style.color = "#721c24";
} else {
resultDiv.textContent = "x = " + x.toFixed(4); // Display with 4 decimal places for precision
resultDiv.style.backgroundColor = "#d4edda";
resultDiv.style.borderColor = "#c3e6cb";
resultDiv.style.color = "#155724";
}
}