Math Problem Statement

What does the mathematical expression |x| represent?

Solution

The uploaded image contains the mathematical expression x|x|, which represents the absolute value of xx.

Explanation:

  1. The absolute value x|x| measures the distance of a number xx from 0 on the number line, without considering the direction (positive or negative).
  2. Mathematically: \begin{cases} x, & \text{if } x \geq 0, \\ -x, & \text{if } x < 0. \end{cases}$$
  3. For example:
    • 5=5|5| = 5 because 505 \geq 0,
    • 3=3|-3| = 3 because 3<0-3 < 0.

Let me know if you want additional details or have further questions!

Follow-up Questions:

  1. How do you solve equations involving absolute values, like x=5|x| = 5?
  2. What is the geometric interpretation of absolute values on a number line?
  3. How does x|x| behave in inequalities, e.g., x<3|x| < 3?
  4. Can you define absolute value for complex numbers?
  5. How do you graph x|x| as a function?

Tip:

Absolute value functions are always non-negative; they are often used in real-world problems like distance, error measurements, and optimization.

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Math Problem Analysis

Mathematical Concepts

Absolute Value
Number Line
Inequalities

Formulas

|x| = x, if x ≥ 0
|x| = -x, if x < 0

Theorems

Definition of Absolute Value

Suitable Grade Level

Grades 6-8