Solve Inequality and Write in Interval Notation Calculator

How to Use This Calculator

Using our inequality solver is straightforward. Follow these steps to get accurate results:

1. Enter the inequality in the input field. For example, you might enter "x + 3 > 5".
2. Click the "Calculate" button to solve the inequality.
3. Review the solution in interval notation displayed below the calculator.
4. Use the "Reset" button to clear the form and start a new calculation.

The calculator handles basic linear inequalities with one variable. For more complex inequalities, you may need to solve them manually or use a more advanced mathematical tool.

How the Calculator Works

The calculator follows a systematic approach to solve linear inequalities:

1. Input Validation: The calculator first checks if the input is a valid linear inequality.
2. Isolate the Variable: The calculator isolates the variable (usually x) by performing inverse operations.
3. Determine the Solution: Based on the inequality sign, the calculator determines the range of values that satisfy the inequality.
4. Interval Notation: The solution is then expressed in interval notation, which is a concise way to represent ranges of numbers.

The calculator uses these steps to provide accurate and reliable results for any valid linear inequality you input.

Worked Examples

Let's look at a few examples to understand how the calculator works in practice.

Example 1: Simple Inequality

Inequality: 2x + 3 < 11

1. Subtract 3 from both sides: 2x < 8
2. Divide both sides by 2: x < 4
3. Interval notation: (-∞, 4)

Example 2: Inequality with Division

Inequality: (x - 2)/3 ≥ 4

1. Multiply both sides by 3: x - 2 ≥ 12
2. Add 2 to both sides: x ≥ 14
3. Interval notation: [14, ∞)

Example 3: Compound Inequality

Inequality: -3 ≤ 2x + 1 < 7

1. Subtract 1 from all parts: -4 ≤ 2x < 6
2. Divide all parts by 2: -2 ≤ x < 3
3. Interval notation: [-2, 3)

Common Mistakes to Avoid

When solving inequalities, it's easy to make mistakes. Here are some common pitfalls to watch out for:

• Forgetting to Reverse the Inequality Sign: When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign. For example, if you have x/2 > 3 and you multiply both sides by -1, you must write -x/2 < -3.
• Incorrectly Handling Compound Inequalities: Compound inequalities require careful handling. Make sure to perform the same operation on all parts of the inequality. For example, if you have 1 < x + 3 < 5, subtracting 3 from all parts gives -2 < x < 2.
• Misinterpreting Interval Notation: Interval notation can be confusing. Remember that parentheses ( ) indicate that the endpoint is not included, while square brackets [ ] indicate that the endpoint is included. For example, [3, 7) means all numbers from 3 up to but not including 7.