Put Inequality Into Interval Notation Calculator

How to Use This Calculator

Converting inequalities to interval notation is a straightforward process when you follow the correct steps. Here's how to use our calculator effectively:

1. Enter the inequality: In the input field, type the mathematical inequality you want to convert. For example, you might enter x > 3 or -2 ≤ y < 5.
2. Select the variable: Choose the variable from the dropdown menu. This helps the calculator identify which variable you're working with.
3. Click "Convert": Once you've entered the inequality and selected the variable, click the "Convert" button to generate the interval notation.
4. Review the result: The calculator will display the interval notation equivalent of your inequality. You can also see a visual representation of the interval on the number line.
5. Reset or try another inequality: If you want to start over, click the "Reset" button. To convert another inequality, simply enter a new one and click "Convert" again.

The Conversion Process

Understanding how to convert inequalities to interval notation is key to mastering this mathematical concept. Here's a step-by-step guide to the process:

Step 1: Identify the Inequality

The first step is to clearly identify the inequality you want to convert. For example, consider the inequality x > 3. This means that the value of x is greater than 3.

Step 2: Determine the Variable

Next, identify the variable in the inequality. In the example x > 3, the variable is x. This variable will be the focus of your interval notation.

Step 3: Understand the Symbols

Mathematical inequalities use specific symbols to indicate relationships between numbers. Here's what each symbol means:

• < (less than)
• > (greater than)
• ≤ (less than or equal to)
• ≥ (greater than or equal to)

Step 4: Convert to Interval Notation

Once you understand the inequality and the symbols, you can convert it to interval notation. Interval notation uses parentheses and brackets to represent the range of values that satisfy the inequality.

Step 5: Verify the Result

After converting the inequality to interval notation, it's important to verify your result. You can do this by checking the endpoints and the type of brackets used. Parentheses indicate that the endpoint is not included, while brackets indicate that the endpoint is included.

Worked Examples

To help you understand how to convert inequalities to interval notation, here are some worked examples:

Example 1: Simple Inequality

Convert the inequality x > 4 to interval notation.

1. Identify the inequality: x > 4.
2. Determine the variable: x.
3. Understand the symbol: > means greater than.
4. Convert to interval notation: Since x is greater than 4 but not equal to 4, the interval notation is (4, ∞).

Example 2: Compound Inequality

Convert the inequality -3 ≤ y < 2 to interval notation.

1. Identify the inequality: -3 ≤ y < 2.
2. Determine the variable: y.
3. Understand the symbols: ≤ means less than or equal to, and < means less than.
4. Convert to interval notation: Since y is greater than or equal to -3 and less than 2, the interval notation is [-3, 2).

Example 3: Double-Bounded Inequality

Convert the inequality 0 < z ≤ 10 to interval notation.

1. Identify the inequality: 0 < z ≤ 10.
2. Determine the variable: z.
3. Understand the symbols: < means less than, and ≤ means less than or equal to.
4. Convert to interval notation: Since z is greater than 0 and less than or equal to 10, the interval notation is (0, 10].