Enter the coefficients and constants for your linear equation in the form ax + b = c to see the solution for x and the detailed steps involved.
Result:
Steps to Solve:
Understanding Linear Equations and How to Solve Them
A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. The most common form for a single-variable linear equation is ax + b = c, where:
x is the variable you want to solve for.
a is the coefficient of x (a number multiplied by x).
b is a constant term on the same side as x.
c is a constant term on the opposite side of x.
The Goal: Isolate the Variable
The primary goal when solving any linear equation is to isolate the variable (x) on one side of the equation. This means getting x by itself, with a coefficient of 1. To achieve this, we use inverse operations.
Step-by-Step Solving Process:
Eliminate the constant term (b) from the side with x: To do this, you perform the inverse operation of what's currently applied to b. If b is being added, subtract b from both sides of the equation. If b is being subtracted, add b to both sides. This maintains the equality of the equation.
Eliminate the coefficient (a) from x: Once ax is isolated, you need to get rid of the coefficient a. Since a is multiplying x, the inverse operation is division. Divide both sides of the equation by a.
The result: After these steps, you will have x isolated on one side, and its value on the other.
Example Walkthrough:
Let's take the equation 2x + 5 = 15, which is the default example in our calculator:
Original Equation:2x + 5 = 15
Step 1: Subtract 5 from both sides to move the constant term b:
2x + 5 - 5 = 15 - 5
2x = 10
Step 2: Divide both sides by 2 to isolate x:
2x / 2 = 10 / 2
x = 5
So, the solution for x is 5.
This calculator automates these steps, allowing you to quickly solve various linear equations and understand the process behind the solution.
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function calculateEquation() {
var a = parseFloat(document.getElementById("coefficientA").value);
var b = parseFloat(document.getElementById("constantB").value);
var c = parseFloat(document.getElementById("constantC").value);
var resultDiv = document.getElementById("result");
var workStepsDiv = document.getElementById("workSteps");
resultDiv.innerHTML = "";
workStepsDiv.innerHTML = "";
if (isNaN(a) || isNaN(b) || isNaN(c)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
var steps = [];
var currentEquation = a + "x + " + b + " = " + c;
steps.push("Original Equation: " + currentEquation);
// Step 1: Subtract 'b' from both sides
var cMinusB = c – b;
steps.push("Step 1: Subtract " + b + " from both sides.");
steps.push(a + "x + " + b + " – " + b + " = " + c + " – " + b);
steps.push(a + "x = " + cMinusB);
// Step 2: Divide by 'a'
if (a === 0) {
if (cMinusB === 0) {
resultDiv.innerHTML = "Infinite solutions (0x = 0).";
workStepsDiv.innerHTML = steps.join("");
} else {
resultDiv.innerHTML = "No solution (0x = " + cMinusB + ").";
workStepsDiv.innerHTML = steps.join("");
}
return;
}
var x = cMinusB / a;
steps.push("Step 2: Divide both sides by " + a + ".");
steps.push(a + "x / " + a + " = " + cMinusB + " / " + a);
steps.push("x = " + x);
resultDiv.innerHTML = "The value of x is: " + x.toFixed(4) + "";
workStepsDiv.innerHTML = steps.join("");
}