Algebra Equation Solver
Enter your linear equation in the format ax + b = c.
Understanding Linear Equations: The Basics
Linear equations are fundamental in algebra. They represent a relationship between variables where the highest power of the variable is one. The most common form you'll encounter for a single variable, say 'x', is the linear equation. When we solve for 'x', we are trying to find the specific value that makes the equation true.
The Standard Form: ax + b = c
The equation ax + b = c is a standard way to represent a linear equation. Here's what each part means:
x: This is the variable we want to solve for. It's the unknown value.a: This is the coefficient of the variable 'x'. It's the number that multiplies 'x'.b: This is a constant term that is added to the 'ax' term.c: This is the constant on the right-hand side of the equation, representing the total value.
How to Solve ax + b = c Step-by-Step
The goal is to isolate 'x' on one side of the equation. We do this by applying inverse operations to both sides of the equation, ensuring the equality remains balanced. Here's the process:
- Subtract 'b' from both sides: To get rid of the '+ b' term on the left side, we perform the inverse operation, which is subtraction.
ax + b - b = c - b
This simplifies to:ax = c - b - Divide both sides by 'a': Now, 'x' is multiplied by 'a'. To isolate 'x', we perform the inverse operation, division.
ax / a = (c - b) / a
This gives us the solution for 'x':x = (c - b) / a
This formula, x = (c - b) / a, is the direct solution. Our calculator implements these steps to show you how the result is obtained.
Important Considerations:
- Division by Zero: The formula involves dividing by 'a'. If 'a' is zero, the equation is either a contradiction (if
b != c) or an identity (ifb == c), meaning there's no unique solution for 'x' in the typical sense. Our calculator will flag this case. - Input Types: The coefficients and constants can be any real numbers, including positive, negative, decimals, or fractions.
Use Cases:
Solving linear equations is a cornerstone of mathematics and appears in countless applications:
- Physics: Calculating time, distance, or velocity when relationships are linear.
- Finance: Simple interest calculations, budget planning.
- Engineering: Modeling systems with linear relationships.
- Everyday Problems: Figuring out how many items you need to buy to meet a certain budget, or how long a task will take based on a constant rate.
This calculator provides a clear, step-by-step breakdown, making it a valuable tool for students learning algebra or anyone needing to solve simple linear equations quickly and accurately.
" + a + "x + " + b + " - " + b + " = " + c + " - " + b + "";
stepHTML += " Simplifies to: " + a + "x = " + newC + "";
// — Check for division by zero —
if (a === 0) {
if (newC === 0) {
stepHTML += "2. The coefficient 'a' is 0 and the result of step 1 is also 0. This means the original equation is an identity (true for all values of x).";
resultDiv.innerHTML = "The equation is true for all real numbers.";
} else {
stepHTML += "2. The coefficient 'a' is 0, but the result of step 1 is " + newC + ". This means the original equation is a contradiction (there is no solution for x).";
resultDiv.innerHTML = "Error: No solution exists. The equation is a contradiction.";
}
stepDiv.innerHTML = stepHTML;
return;
}
// — Step 2: Divide by a —
var x = newC / a;
stepHTML += "2. Divide both sides by " + a + ":";
stepHTML += " (" + a + "x) / " + a + " = " + newC + " / " + a + "";
stepHTML += " Result: x = " + x + "";
stepDiv.innerHTML = stepHTML;
// Display final result
resultDiv.innerHTML = "The solution is: x = " + x + "";
}