Inequality Math Calculator

Linear Inequality Checker

Use this calculator to check if a specific value for 'X' satisfies a linear inequality in the form aX + b [operator] c.

<option value="< ">> <option value="≤ =">≥

function calculateInequality() { var coefficientA = parseFloat(document.getElementById('coefficientA').value); var variableX = parseFloat(document.getElementById('variableX').value); var constantB = parseFloat(document.getElementById('constantB').value); var inequalityOperator = document.getElementById('inequalityOperator').value; var constantC = parseFloat(document.getElementById('constantC').value); var resultDiv = document.getElementById('inequalityResult'); if (isNaN(coefficientA) || isNaN(variableX) || isNaN(constantB) || isNaN(constantC)) { resultDiv.innerHTML = 'Please enter valid numbers for all fields.'; return; } var leftSideValue = coefficientA * variableX + constantB; var isTrue; switch (inequalityOperator) { case '<': isTrue = leftSideValue ': isTrue = leftSideValue > constantC; break; case '<=': isTrue = leftSideValue =': isTrue = leftSideValue >= constantC; break; default: resultDiv.innerHTML = 'Invalid inequality operator selected.'; return; } var operatorSymbol; switch (inequalityOperator) { case '<': operatorSymbol = '': operatorSymbol = '>'; break; case '=': operatorSymbol = '≥'; break; } var resultText = 'For X = ' + variableX + ', the inequality ' + coefficientA + ' × ' + variableX + ' + ' + constantB + ' (' + leftSideValue + ') ' + operatorSymbol + ' ' + constantC + ' is ' + (isTrue ? 'True' : 'False') + '.'; resultDiv.innerHTML = " + resultText + "; } /* Basic styling for the calculator */ .calculator-container { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; background-color: #f9f9f9; border: 1px solid #ddd; border-radius: 8px; padding: 20px; max-width: 600px; margin: 20px auto; box-shadow: 0 2px 5px rgba(0,0,0,0.1); } .calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; } .calculator-container p { color: #555; line-height: 1.6; margin-bottom: 15px; } .calc-input-group { margin-bottom: 15px; } .calc-input-group label { display: block; margin-bottom: 5px; color: #333; font-weight: bold; } .calc-input-group input[type="number"], .calc-input-group select { width: calc(100% – 22px); /* Account for padding and border */ padding: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; font-size: 16px; } .calc-input-group select { width: 100%; } .calculator-container button { display: block; width: 100%; padding: 12px 20px; background-color: #007bff; color: white; border: none; border-radius: 4px; font-size: 18px; cursor: pointer; transition: background-color 0.3s ease; margin-top: 20px; } .calculator-container button:hover { background-color: #0056b3; } .calc-result { margin-top: 25px; padding: 15px; background-color: #e9f7ef; border: 1px solid #d4edda; border-radius: 4px; color: #155724; font-size: 1.1em; text-align: center; word-wrap: break-word; } .calc-result p { margin: 0; color: #155724; } .calc-result .error { color: #721c24; background-color: #f8d7da; border-color: #f5c6cb; padding: 10px; border-radius: 4px; } code { background-color: #eee; padding: 2px 4px; border-radius: 3px; font-family: monospace; }

Understanding Linear Inequalities

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used to compare quantities that are not equal. Unlike equations, which use an equals sign (=), inequalities use symbols like less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥).

What is a Linear Inequality?

A linear inequality is an inequality that involves a linear function. It is an algebraic expression in which each term has at most one variable, and the highest power of any variable is 1. A common form of a linear inequality with one variable is aX + b [operator] c, where:

• a is the coefficient of the variable X.
• X is the variable.
• b is a constant term on the left side.
• [operator] is one of the inequality symbols (<, >, ≤, ≥).
• c is a constant term on the right side.

For example, 2X + 3 < 15 is a linear inequality. Here, a=2, b=3, and c=15.

How to Check if a Value Satisfies an Inequality

To determine if a specific value for the variable (X) satisfies a linear inequality, you substitute that value into the inequality and then evaluate both sides. If the resulting statement is true, then the value satisfies the inequality. If it's false, it does not.

Step-by-Step Example:

Let's use the inequality 2X + 3 < 15 and check if X = 5 satisfies it.

1. Identify the components:
   • Coefficient of X (a) = 2
   • Value for X = 5
   • Constant Term (b) = 3
   • Inequality Operator = <
   • Right Side Constant (c) = 15
2. Substitute the value of X into the left side:

   2 * (5) + 3

3. Calculate the left side:

   10 + 3 = 13

4. Compare the calculated left side with the right side using the operator:

   Is 13 < 15?

5. Determine truthfulness:

   Yes, 13 is indeed less than 15. Therefore, the statement is True.

This means that X = 5 is a solution to the inequality 2X + 3 < 15.

Using the Linear Inequality Checker

Our calculator simplifies this process. Simply input the coefficient of X, the value you want to test for X, the constant term on the left, choose your inequality operator, and input the constant on the right. The calculator will instantly tell you whether the inequality holds true for your given X value.

Why are Inequalities Important?

Inequalities are fundamental in various fields:

• Mathematics: Used in algebra, calculus, and optimization problems to define ranges of possible values.
• Science and Engineering: Essential for modeling physical constraints, tolerances, and conditions (e.g., a bridge can withstand a load of 'X' tons, where X ≤ maximum load).
• Economics and Business: Used to represent budget constraints, profit maximization, and resource allocation (e.g., production must be at least 'Y' units to break even).
• Computer Science: Crucial in algorithms, conditional statements, and data filtering.

Understanding and working with inequalities allows us to describe situations where quantities are not necessarily equal but have a specific relationship (e.g., one is larger than the other, or at least as large).