Math Problem Statement
What does the mathematical expression |x| represent?
Solution
The uploaded image contains the mathematical expression , which represents the absolute value of .
Explanation:
- The absolute value measures the distance of a number from 0 on the number line, without considering the direction (positive or negative).
- Mathematically: \begin{cases} x, & \text{if } x \geq 0, \\ -x, & \text{if } x < 0. \end{cases}$$
- For example:
- because ,
- because .
Let me know if you want additional details or have further questions!
Follow-up Questions:
- How do you solve equations involving absolute values, like ?
- What is the geometric interpretation of absolute values on a number line?
- How does behave in inequalities, e.g., ?
- Can you define absolute value for complex numbers?
- How do you graph 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