Best Calculator for Algebra 1: Solve Equations Easily
:root {
–primary-color: #004a99;
–background-color: #f8f9fa;
–card-background: #ffffff;
–text-color: #333;
–border-color: #ddd;
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body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–background-color);
color: var(–text-color);
margin: 0;
padding: 0;
line-height: 1.6;
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max-width: 960px;
margin: 20px auto;
padding: 20px;
background-color: var(–card-background);
border-radius: 8px;
box-shadow: 0 2px 10px var(–shadow-color);
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header {
text-align: center;
padding-bottom: 20px;
border-bottom: 1px solid var(–border-color);
margin-bottom: 20px;
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header h1 {
color: var(–primary-color);
margin-bottom: 10px;
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margin-bottom: 30px;
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margin-top: 0;
margin-bottom: 20px;
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.input-group {
margin-bottom: 15px;
text-align: left;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: var(–primary-color);
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.input-group input[type="number"],
.input-group input[type="text"],
.input-group select {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid var(–border-color);
border-radius: 4px;
box-sizing: border-box;
font-size: 1rem;
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.input-group .helper-text {
font-size: 0.85em;
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color: #dc3545;
font-size: 0.85em;
margin-top: 5px;
display: block;
min-height: 1.2em; /* Prevent layout shift */
}
.button-group {
display: flex;
justify-content: space-between;
margin-top: 20px;
gap: 10px;
}
.button-group button {
flex-grow: 1;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 1rem;
font-weight: bold;
transition: background-color 0.3s ease;
}
.calculate-button {
background-color: var(–primary-color);
color: white;
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.calculate-button:hover {
background-color: #003366;
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.reset-button {
background-color: #6c757d;
color: white;
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color: white;
}
.copy-button:hover {
background-color: #218838;
}
.results-container {
margin-top: 25px;
padding: 15px;
border: 1px solid var(–border-color);
border-radius: 8px;
background-color: #e9ecef;
text-align: center;
}
.results-container h3 {
color: var(–primary-color);
margin-top: 0;
margin-bottom: 15px;
}
.primary-result {
font-size: 2em;
font-weight: bold;
color: var(–primary-color);
margin-bottom: 10px;
display: block;
}
.intermediate-results div {
margin-bottom: 8px;
font-size: 1.1em;
}
.formula-explanation {
font-size: 0.9em;
color: #555;
margin-top: 15px;
padding-top: 10px;
border-top: 1px solid var(–border-color);
}
table {
width: 100%;
border-collapse: collapse;
margin-top: 20px;
}
th, td {
padding: 10px;
text-align: left;
border: 1px solid var(–border-color);
}
thead {
background-color: var(–primary-color);
color: white;
}
tbody tr:nth-child(even) {
background-color: #f2f2f2;
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overflow-x: auto;
margin-top: 20px;
border: 1px solid var(–border-color);
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caption {
caption-side: bottom;
text-align: center;
padding: 10px;
font-size: 0.9em;
color: #555;
}
canvas {
max-width: 100%;
height: auto;
display: block;
margin: 20px auto;
border: 1px solid var(–border-color);
border-radius: 4px;
}
.article-section {
margin-top: 30px;
padding: 20px;
background-color: var(–card-background);
border-radius: 8px;
box-shadow: 0 2px 10px var(–shadow-color);
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.article-section h2, .article-section h3 {
color: var(–primary-color);
margin-bottom: 15px;
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.article-section p {
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.article-section ul {
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margin-bottom: 15px;
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.article-section li {
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padding-top: 20px;
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.container {
margin: 10px;
padding: 15px;
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.button-group {
flex-direction: column;
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.button-group button {
width: 100%;
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}
Algebra 1 Equation Solver
Results
—
This calculator uses algebraic manipulation to isolate the specified variable.
It performs operations like addition, subtraction, multiplication, and division on both sides of the equation to find the value of the variable.
Equation Visualization
Visual representation of the equation's balance.
What is Algebra 1?
Algebra 1 is a foundational course in mathematics that introduces students to the fundamental concepts of algebra. It bridges the gap between arithmetic and more advanced mathematical subjects like geometry, trigonometry, and calculus. In Algebra 1, you learn to work with variables, expressions, equations, and inequalities. The primary goal is to develop the ability to represent mathematical relationships using symbols and to solve problems by manipulating these symbols. This course is crucial for understanding how mathematical models can describe real-world phenomena and for developing critical thinking and problem-solving skills. Mastering Algebra 1 concepts is essential for success in higher-level mathematics and many STEM fields.
Algebra 1 Formula and Mathematical Explanation
The core of Algebra 1 revolves around solving equations and inequalities. An equation is a statement that two mathematical expressions are equal, typically involving one or more variables. The fundamental principle is to maintain balance: whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side. This ensures the equality remains true.
For a linear equation in one variable, like ax + b = c, the goal is to isolate the variable 'x'. The process involves a series of inverse operations:
- Subtraction/Addition: To remove a constant term (like 'b'), you subtract or add it from both sides. For example, in
2x + 5 = 11, subtract 5 from both sides: 2x = 11 - 5, which simplifies to 2x = 6.
- Division/Multiplication: To remove a coefficient (like 'a'), you divide or multiply both sides by that coefficient. Continuing the example, divide both sides by 2:
x = 6 / 2, resulting in x = 3.
The formula isn't a single equation but a systematic approach. If the equation is ax + b = c, the solution for x is derived as:
ax = c - b
x = (c - b) / a
This general form allows us to solve any linear equation of this type. Understanding this systematic approach is key to solving a wide range of algebraic problems. This is precisely what the best calculator for Algebra 1 aims to automate and visualize.
Practical Examples (Real-World Use Cases)
Algebra 1 concepts are surprisingly prevalent in everyday life and various professions. Here are a few practical examples:
- Budgeting: If you have a total budget (C) and fixed expenses (b), and you want to save a certain amount per week (a) to reach your goal in 'x' weeks, you can use an equation like
ax + b = C to find out how many weeks it will take.
- Cooking and Recipes: Scaling recipes often involves algebraic thinking. If a recipe serves 4 people and you need it to serve 10, you need to find a scaling factor. This is akin to solving a proportion, a core Algebra 1 skill.
- Distance, Rate, and Time: The classic formula
distance = rate × time (d = rt) is a fundamental algebraic relationship. If you know the distance and the rate, you can solve for time (t = d/r), or if you know distance and time, you can solve for rate (r = d/t). This is essential for planning trips or understanding travel logistics.
- Physics and Engineering: Many basic physics formulas, like Ohm's Law (
V = IR) in electricity, are linear equations. Engineers use these to calculate voltage, current, or resistance.
- Personal Finance: Calculating simple interest involves algebraic formulas. If you want to know how long it will take for an investment to grow to a certain amount, you'll use algebraic manipulation. Understanding these principles helps in making informed financial decisions.
These examples highlight how the skills learned in Algebra 1 are not just academic exercises but practical tools for navigating the world. Using a reliable Algebra 1 calculator can help solidify understanding of these applications.
How to Use This Algebra 1 Calculator
Using this calculator is straightforward and designed to help you understand the process of solving algebraic equations. Follow these simple steps:
- Enter the Equation: In the "Enter Equation" field, type the algebraic equation you want to solve. Use standard mathematical notation. For example, type
2x + 5 = 11 or 3(y - 2) = 9.
- Specify the Variable: In the "Variable to Solve For" field, enter the variable you wish to isolate. By default, it's set to 'x', but you can change it to 'y', 'z', or any other variable present in your equation.
- Calculate: Click the "Calculate Solution" button. The calculator will process your input.
- View Results: The primary result (the value of the variable) will be displayed prominently. You'll also see key intermediate values and a step-by-step breakdown of the solution process in the table. The chart provides a visual representation.
- Copy Results: If you need to save or share the results, click the "Copy Results" button. This will copy the main solution, intermediate values, and key assumptions to your clipboard.
- Reset: To clear the fields and start over, click the "Reset" button. It will revert the inputs to their default sensible values.
This tool is an excellent resource for checking your homework, understanding different solution methods, or exploring how changes in an equation affect the outcome. It's one of the best tools for anyone learning or practicing Algebra 1.
Key Factors That Affect Algebra 1 Results
While this calculator automates the process, understanding the factors that influence the results is crucial for true mathematical comprehension. These factors relate directly to the structure and components of the equation itself:
- Complexity of the Equation: Simple linear equations like
x + 5 = 10 are easier to solve than multi-step equations involving parentheses, fractions, or multiple instances of the variable on both sides (e.g., 3x - 7 = x + 5). The number of steps required to isolate the variable directly impacts the complexity.
- Presence of Parentheses: Equations with parentheses often require the distributive property first (e.g.,
2(x + 3) = 10). This adds an initial step before standard isolation techniques can be applied.
- Fractions and Decimals: Working with fractions or decimals can introduce calculation errors if not handled carefully. Clearing fractions by multiplying by the least common denominator or converting decimals can simplify the process, but these operations themselves are critical steps.
- Coefficients and Constants: The values of the coefficients (the numbers multiplying the variables) and constants (the standalone numbers) determine the specific operations needed. A coefficient of 0, for instance, would fundamentally change the nature of the equation.
- Variable Placement: If the variable appears on both sides of the equation (e.g.,
5x = 2x + 9), an extra step is needed to gather all variable terms on one side before proceeding with isolation.
- Type of Equation: This calculator is primarily designed for linear equations. Quadratic equations (involving x²) or higher-order polynomials require different solution methods (like factoring, quadratic formula, or graphing) and are beyond the scope of this specific tool.
Understanding these factors helps in anticipating the steps needed and in verifying the calculator's output. It reinforces the importance of careful algebraic manipulation, a key skill in Algebra 1.
Frequently Asked Questions (FAQ)
Q1: What is the difference between an expression and an equation?
An expression is a combination of numbers, variables, and operations (like 2x + 5) that represents a value but doesn't state equality. An equation, on the other hand, is a statement that two expressions are equal (like 2x + 5 = 11) and can be solved for the variable.
Q2: Can this calculator solve equations with variables on both sides?
Yes, this calculator is designed to handle linear equations where the variable might appear on both sides of the equals sign. It will perform the necessary steps to gather variable terms on one side.
Q3: What if my equation involves fractions?
The calculator attempts to handle common algebraic forms, including those that might implicitly involve fractions during the solving process. For complex fractional equations, it's best to simplify them manually first or use a more specialized tool.
Q4: How accurate is the calculator?
The calculator uses standard algebraic algorithms and should provide accurate results for solvable linear equations within typical computational precision. However, always double-check complex problems or critical calculations.
Q5: Can this calculator solve quadratic equations (e.g., x² + 2x + 1 = 0)?
No, this specific calculator is designed for linear equations (where the highest power of the variable is 1). Solving quadratic equations requires different methods like factoring or the quadratic formula.
Q6: Why is Algebra 1 important?
Algebra 1 is crucial because it develops logical reasoning, problem-solving skills, and provides the foundation for all higher-level mathematics and many science and technology fields. It teaches you how to think abstractly and systematically.
Related Tools and Internal Resources
var equationInput = document.getElementById('equation');
var variableInput = document.getElementById('variable');
var equationError = document.getElementById('equationError');
var variableError = document.getElementById('variableError');
var primaryResultDiv = document.getElementById('primaryResult');
var intermediate1Div = document.getElementById('intermediate1');
var intermediate2Div = document.getElementById('intermediate2');
var intermediate3Div = document.getElementById('intermediate3');
var solutionTableBody = document.querySelector('#solutionTable tbody');
var equationChartCanvas = document.getElementById('equationChart');
var chartInstance = null;
function isValidVariable(str) {
return /^[a-zA-Z]$/.test(str);
}
function parseEquation(equationStr, variable) {
equationStr = equationStr.replace(/\s+/g, "); // Remove whitespace
var parts = equationStr.split('=');
if (parts.length !== 2) {
return { error: "Invalid equation format. Must contain exactly one '=' sign." };
}
var leftSide = parts[0];
var rightSide = parts[1];
// Basic check for variable existence
if (leftSide.indexOf(variable) === -1 && rightSide.indexOf(variable) === -1) {
return { error: "The specified variable '" + variable + "' is not found in the equation." };
}
// Attempt to evaluate expressions using a simplified approach or a library if available
// For this example, we'll use a simplified parser for linear equations ax + b = c or similar
// A robust parser is complex; this is a placeholder for demonstration.
// We'll focus on the structure ax + b = c or ax = c or x + b = c
var regexLinear = new RegExp('^([+-]?\\d*\\.?\\d*)' + variable + '([+-]\\d+\\.?\\d*)$'); // Matches like 2x+5, -3x-10
var regexLinearSimple = new RegExp('^([+-]?\\d*\\.?\\d*)' + variable + '$'); // Matches like 2x, -5x
var regexConstant = new RegExp('^([+-]?\\d+\\.?\\d*)$'); // Matches like 5, -10.5
var leftParts = parseSide(leftSide, variable);
var rightParts = parseSide(rightSide, variable);
if (leftParts.error) return { error: "Error parsing left side: " + leftParts.error };
if (rightParts.error) return { error: "Error parsing right side: " + rightParts.error };
// Combine terms: (a_left – a_right) * variable + (b_left – b_right) = 0
var totalVarCoeff = leftParts.varCoeff – rightParts.varCoeff;
var totalConst = leftParts.constTerm – rightParts.constTerm;
if (totalVarCoeff === 0) {
if (totalConst === 0) {
return { error: "Equation is an identity (true for all values of " + variable + "). Cannot determine a unique solution." };
} else {
return { error: "Equation is a contradiction (no solution exists)." };
}
}
var solutionValue = -totalConst / totalVarCoeff;
return { solution: solutionValue, steps: generateSteps(leftSide, rightSide, variable, totalVarCoeff, totalConst) };
}
function parseSide(sideStr, variable) {
var varCoeff = 0;
var constTerm = 0;
// Try to find terms like ax, bx, etc.
var varRegex = new RegExp('([+-]?(?:\\d*\\.?\\d+)?' + variable + ')', 'g');
var matches = sideStr.match(varRegex);
if (matches) {
matches.forEach(function(match) {
var coeffStr = match.replace(variable, ");
if (coeffStr === " || coeffStr === '+') varCoeff += 1;
else if (coeffStr === '-') varCoeff -= 1;
else varCoeff += parseFloat(coeffStr);
sideStr = sideStr.replace(match, "); // Remove matched variable term
});
}
// Remaining parts should be constants
var constRegex = /([+-]?\d+\.?\d*)/g;
var constMatches = sideStr.match(constRegex);
if (constMatches) {
constMatches.forEach(function(match) {
constTerm += parseFloat(match);
});
}
// Check if anything is left that wasn't parsed
var remaining = sideStr.replace(varRegex, ").replace(constRegex, ").replace(/[+-]/g, ");
if (remaining.length > 0) {
return { error: "Could not parse remaining characters: '" + remaining + "'" };
}
return { varCoeff: varCoeff, constTerm: constTerm };
}
function generateSteps(leftSide, rightSide, variable, totalVarCoeff, totalConst) {
var steps = [];
var currentLeftSide = leftSide;
var currentRightSide = rightSide;
var stepCount = 1;
// Step 1: Move variable terms to one side (e.g., left)
var leftVarCoeff = parseSide(currentLeftSide, variable).varCoeff;
var rightVarCoeff = parseSide(currentRightSide, variable).varCoeff;
var leftConstTerm = parseSide(currentLeftSide, variable).constTerm;
var rightConstTerm = parseSide(currentRightSide, variable).constTerm;
var operation = "";
var equationState = "";
if (rightVarCoeff !== 0) {
operation = "Subtract " + rightVarCoeff + variable + " from both sides.";
var newLeftSide = (leftVarCoeff – rightVarCoeff) + variable + (leftConstTerm >= 0 ? "+" + leftConstTerm : leftConstTerm);
var newRightSide = rightConstTerm;
steps.push({ step: stepCount++, operation: operation, state: currentLeftSide + " = " + currentRightSide + " -> " + newLeftSide + " = " + newRightSide });
currentLeftSide = newLeftSide;
currentRightSide = newRightSide;
}
// Step 2: Move constant terms to the other side (e.g., right)
var leftConstTermCurrent = parseSide(currentLeftSide, variable).constTerm;
var rightConstTermCurrent = parseSide(currentRightSide, variable).constTerm;
var leftVarCoeffCurrent = parseSide(currentLeftSide, variable).varCoeff;
if (leftConstTermCurrent !== 0) {
operation = "Subtract " + leftConstTermCurrent + " from both sides.";
var newLeftSide = leftVarCoeffCurrent + variable;
var newRightSide = (rightConstTermCurrent – leftConstTermCurrent);
steps.push({ step: stepCount++, operation: operation, state: currentLeftSide + " = " + currentRightSide + " -> " + newLeftSide + " = " + newRightSide });
currentLeftSide = newLeftSide;
currentRightSide = newRightSide;
}
// Step 3: Isolate the variable by dividing by its coefficient
var finalVarCoeff = parseSide(currentLeftSide, variable).varCoeff;
var finalConst = parseSide(currentRightSide, variable).constTerm;
if (finalVarCoeff !== 1 && finalVarCoeff !== -1) {
operation = "Divide both sides by " + finalVarCoeff + ".";
var newLeftSide = variable;
var newRightSide = finalConst / finalVarCoeff;
steps.push({ step: stepCount++, operation: operation, state: currentLeftSide + " = " + currentRightSide + " -> " + newLeftSide + " = " + newRightSide });
currentLeftSide = newLeftSide;
currentRightSide = newRightSide;
} else if (finalVarCoeff === -1) {
operation = "Multiply both sides by -1.";
var newLeftSide = variable;
var newRightSide = finalConst * -1;
steps.push({ step: stepCount++, operation: operation, state: currentLeftSide + " = " + currentRightSide + " -> " + newLeftSide + " = " + newRightSide });
currentLeftSide = newLeftSide;
currentRightSide = newRightSide;
}
return steps;
}
function calculateSolution() {
var equation = equationInput.value;
var variable = variableInput.value;
var errors = false;
// Reset errors
equationError.textContent = ";
variableError.textContent = ";
if (!equation) {
equationError.textContent = 'Equation cannot be empty.';
errors = true;
}
if (!variable) {
variableError.textContent = 'Variable cannot be empty.';
errors = true;
} else if (!isValidVariable(variable)) {
variableError.textContent = 'Please enter a single letter for the variable.';
errors = true;
}
if (errors) {
primaryResultDiv.textContent = '–';
intermediate1Div.textContent = ";
intermediate2Div.textContent = ";
intermediate3Div.textContent = ";
solutionTableBody.innerHTML = ";
updateChart([], []);
return;
}
var result = parseEquation(equation, variable);
if (result.error) {
equationError.textContent = result.error;
primaryResultDiv.textContent = 'Error';
intermediate1Div.textContent = ";
intermediate2Div.textContent = ";
intermediate3Div.textContent = ";
solutionTableBody.innerHTML = ";
updateChart([], []);
} else {
var solutionValue = result.solution;
var steps = result.steps || [];
primaryResultDiv.textContent = variable + ' = ' + solutionValue.toFixed(4); // Display with 4 decimal places
// Intermediate values – simplified for linear equations
var intermediate1 = "Original Equation: " + equation;
var intermediate2 = "Variable Isolated: " + variable + " = " + solutionValue.toFixed(4);
var intermediate3 = "Check: Substitute " + solutionValue.toFixed(4) + " back into the original equation.";
intermediate1Div.textContent = intermediate1;
intermediate2Div.textContent = intermediate2;
intermediate3Div.textContent = intermediate3;
// Populate table
solutionTableBody.innerHTML = ";
steps.forEach(function(step) {
var row = solutionTableBody.insertRow();
row.insertCell(0).textContent = step.step;
row.insertCell(1).textContent = step.operation;
row.insertCell(2).textContent = step.state;
});
// Update chart data
var chartLabels = [];
var chartData = [];
var chartData2 = []; // For original equation side vs solved value
// Add initial state for chart
var initialParsed = parseSide(equation.split('=')[0], variable);
chartLabels.push("Start");
chartData.push(initialParsed.varCoeff * solutionValue + initialParsed.constTerm); // Left side value at solution
chartData2.push(0); // Represents the right side (which becomes 0 after moving terms)
// Add intermediate steps to chart if available
for (var i = 0; i ');
if (stateParts.length === 2) {
var currentEq = stateParts[1].trim();
var eqParts = currentEq.split('=');
if (eqParts.length === 2) {
var label = "Step " + (i + 1);
chartLabels.push(label);
var parsedSide = parseSide(eqParts[0], variable);
chartData.push(parsedSide.varCoeff * solutionValue + parsedSide.constTerm);
chartData2.push(parseFloat(eqParts[1].trim()));
}
}
}
// Ensure the final step is represented correctly
if (steps.length > 0) {
var finalState = steps[steps.length – 1].state.split('->')[1].trim();
var finalParts = finalState.split('=');
if (finalParts.length === 2) {
chartLabels.push("Final");
var parsedSide = parseSide(finalParts[0], variable);
chartData.push(parsedSide.varCoeff * solutionValue + parsedSide.constTerm); // Should be close to 0
chartData2.push(parseFloat(finalParts[1].trim())); // Should be close to 0
}
}
updateChart(chartLabels, chartData, chartData2, variable);
}
}
function updateChart(labels, data1, data2, variable) {
if (!equationChartCanvas) return;
var ctx = equationChartCanvas.getContext('2d');
// Destroy previous chart instance if it exists
if (chartInstance) {
chartInstance.destroy();
}
if (data1.length === 0) {
ctx.clearRect(0, 0, equationChartCanvas.width, equationChartCanvas.height); // Clear canvas if no data
return;
}
chartInstance = new Chart(ctx, {
type: 'line',
data: {
labels: labels,
datasets: [{
label: 'Left Side Value (at solution)',
data: data1,
borderColor: 'rgb(75, 192, 192)',
tension: 0.1,
fill: false
}, {
label: 'Right Side Value',
data: data2,
borderColor: 'rgb(255, 99, 132)',
tension: 0.1,
fill: false
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: false // Adjust based on data range
}
},
plugins: {
title: {
display: true,
text: 'Equation Balance Visualization'
},
legend: {
display: true
}
}
}
});
}
function resetCalculator() {
equationInput.value = '2x + 5 = 11';
variableInput.value = 'x';
equationError.textContent = ";
variableError.textContent = ";
primaryResultDiv.textContent = '–';
intermediate1Div.textContent = ";
intermediate2Div.textContent = ";
intermediate3Div.textContent = ";
solutionTableBody.innerHTML = ";
if (chartInstance) {
chartInstance.destroy();
chartInstance = null;
}
// Clear canvas if no data
var ctx = equationChartCanvas.getContext('2d');
ctx.clearRect(0, 0, equationChartCanvas.width, equationChartCanvas.height);
}
function copyResults() {
var mainResult = primaryResultDiv.textContent;
var intermediate1 = intermediate1Div.textContent;
var intermediate2 = intermediate2Div.textContent;
var intermediate3 = intermediate3Div.textContent;
var formula = document.querySelector('.formula-explanation').textContent;
var textToCopy = "Algebra 1 Calculator Results:\n\n";
textToCopy += "Primary Result: " + mainResult + "\n";
textToCopy += "Intermediate 1: " + intermediate1 + "\n";
textToCopy += "Intermediate 2: " + intermediate2 + "\n";
textToCopy += "Intermediate 3: " + intermediate3 + "\n\n";
textToCopy += "Formula Used: " + formula + "\n";
// Use navigator.clipboard for modern browsers
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(textToCopy).then(function() {
alert('Results copied to clipboard!');
}).catch(function(err) {
console.error('Failed to copy text: ', err);
fallbackCopyTextToClipboard(textToCopy);
});
} else {
fallbackCopyTextToClipboard(textToCopy);
}
}
function fallbackCopyTextToClipboard(text) {
var textArea = document.createElement("textarea");
textArea.value = text;
textArea.style.position = "fixed"; // Avoid scrolling to bottom
textArea.style.left = "-9999px";
textArea.style.top = "-9999px";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'successful' : 'unsuccessful';
console.log('Fallback: Copying text command was ' + msg);
alert('Results copied to clipboard!');
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
alert('Failed to copy results. Please copy manually.');
}
document.body.removeChild(textArea);
}
// Initial calculation on load if there are default values
document.addEventListener('DOMContentLoaded', function() {
// Add Chart.js library dynamically
var script = document.createElement('script');
script.src = 'https://cdn.jsdelivr.net/npm/chart.js';
script.onload = function() {
// Now that Chart.js is loaded, perform initial calculation
calculateSolution();
};
document.head.appendChild(script);
// Add event listeners for real-time updates (optional, but good UX)
equationInput.addEventListener('input', calculateSolution);
variableInput.addEventListener('input', calculateSolution);
});