The inequality \(|x| < -2\) involves the absolute value of \(x\).

By definition, the absolute value \(|x|\) of any real number \(x\) is always non-negative, meaning \(|x| \geq 0\). It cannot be negative. Therefore, the inequality \(|x| < -2\) asks for a non-negative number (the absolute value) to be less than \(-2\), which is impossible.

Thus, there are no real numbers \(x\) that satisfy this inequality. The solution set is:

\[
\text{No solution} \quad \text{or} \quad \emptyset
\]

Would you like more details or have any questions about this solution? Here are five more questions you might be interested in:

1. How do you solve inequalities involving absolute values?
2. What happens when you compare absolute values to negative numbers?
3. How do you solve absolute value equations?
4. Can absolute value inequalities have no solution?
5. How do you interpret absolute value on a number line?

**Tip:** Always remember that the absolute value of a number is non-negative, so inequalities involving negative numbers can often lead to no solutions.

Explore the solution to the absolute value inequality |x| < -2. Understand why this inequality has no real solutions and learn about the properties of absolute values in inequalities. Suitable for high school students studying absolute values and inequalities.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation