Solve linear equations of the form ax + b = c or ax = b.
Solution
Enter values above and click 'Solve Equation'.
Understanding Algebra Equations
Algebraic equations are fundamental tools in mathematics used to represent unknown quantities and relationships between them. A linear equation in one variable, typically represented as ax + b = c, is one of the simplest yet most powerful forms. In this equation:
x is the variable or unknown we want to solve for.
a is the coefficient of the variable x, meaning it's the number multiplied by x.
b is a constant term added to the term with the variable.
c is the constant term that the expression ax + b equals.
The goal of solving such an equation is to find the value of x that makes the equation true. This is achieved by isolating the variable x on one side of the equation using inverse operations.
How the Calculator Works (Solving ax + b = c)
Our calculator solves equations in the form ax + b = c. Here's the mathematical process:
Isolate the 'ax' term: Subtract b from both sides of the equation:
ax + b - b = c - b This simplifies to: ax = c - b
Solve for 'x': Divide both sides by the coefficient a:
ax / a = (c - b) / a This gives the solution: x = (c - b) / a
A special case is when b = 0, reducing the equation to ax = c. The calculator handles this implicitly, as c - 0 is just c.
Important Considerations:
Coefficient 'a' cannot be zero: If a is 0, the equation either becomes 0 = c - b (which is either true for all x if c=b, or false if c!=b) or 0 = c. Division by zero is undefined, so the calculator will indicate an error if a is 0.
Input Validation: The calculator checks if valid numerical inputs are provided for a, b, and c.
Use Cases:
Solving linear equations is a foundational skill used across many disciplines:
Physics: Calculating time, velocity, or distance when relationships are linear.
Finance: Determining break-even points or simple cost calculations.
Engineering: Modeling basic systems and relationships.
Everyday Problems: Figuring out quantities, proportions, or rates.
Example Calculation:
Let's solve the equation 3x + 7 = 22 using the calculator:
Coefficient 'a': 3
Constant 'b': 7
Result 'c': 22
Calculation Steps:
Subtract b (7) from c (22): 22 - 7 = 15. So, 3x = 15.
Divide the result (15) by a (3): 15 / 3 = 5.
The solution is x = 5.
function solveEquation() {
var a = parseFloat(document.getElementById('coefficientA').value);
var b = parseFloat(document.getElementById('constantB').value);
var c = parseFloat(document.getElementById('resultC').value);
var solutionDiv = document.getElementById('solution');
// Clear previous error messages or results
solutionDiv.textContent = ";
solutionDiv.style.color = '#28a745'; // Reset to success color
// Input validation
if (isNaN(a) || isNaN(b) || isNaN(c)) {
solutionDiv.textContent = 'Error: Please enter valid numbers for all fields.';
solutionDiv.style.color = 'red';
return;
}
// Handle the special case where 'a' is 0
if (a === 0) {
if (c === b) {
solutionDiv.textContent = 'Infinite solutions (0 = 0)';
solutionDiv.style.color = 'orange';
} else {
solutionDiv.textContent = 'No solution (' + c + ' != ' + b + ')';
solutionDiv.style.color = 'red';
}
return;
}
// Calculate x for ax + b = c => ax = c – b => x = (c – b) / a
var x = (c – b) / a;
// Display the solution
solutionDiv.textContent = 'x = ' + x;
}