1. What is Absolute Value Interval Notation?

Absolute value inequalities can be expressed using interval notation, which provides a concise way to represent sets of real numbers. The absolute value |x| represents the distance of x from zero on the number line.

2. How Does the Calculator Work?

The calculator solves absolute value inequalities and converts them to interval notation:

Where:

• \( a \) — A positive real number
• \( x \) — The variable being solved for
• Parentheses ( ) indicate endpoints not included
• Brackets [ ] indicate endpoints included

3. Importance of Interval Notation

Details: Interval notation provides a compact, standardized way to express solution sets of inequalities, making it easier to communicate mathematical solutions and visualize them on a number line.

4. Using the Calculator

Tips: Enter a positive value for 'a' and select the type of inequality. The calculator will provide the solution in both interval notation and inequality form.

5. Frequently Asked Questions (FAQ)

Q1: What if 'a' is negative?
A: The absolute value is always non-negative, so inequalities like |x| < -a have no solution when a is positive.

Q2: How is interval notation different from inequality notation?
A: Interval notation uses brackets/parentheses to describe ranges, while inequalities use inequality symbols. Both convey the same information but in different formats.

Q3: What does the ∪ symbol mean?
A: The ∪ symbol represents the union of two sets, meaning "or" in this context.

Q4: How are compound inequalities handled?
A: The calculator automatically converts absolute value inequalities into their equivalent compound inequalities.

Q5: Can this calculator handle more complex absolute value expressions?
A: This version handles basic forms. More complex forms like |ax + b| < c would require additional inputs.