Lesson: Absolute Value

Introduction

Absolute value is a mathematical concept that describes the distance of a number from zero on the number line, regardless of its direction. In symbols, the absolute value of a number $x$ is denoted as $|x|$.

Definition

• For any integer $x$, the absolute value is defined as: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$

Example

• Calculate the absolute values:
  • For $x = 5$:
    $|5| = 5$
  • For $x = -3$:
    $|-3| = -(-3) = 3$
  • For $x = 0$:
    $|0| = 0$

Key Questions

• What is the absolute value of $-7$?
• How does the absolute value change when the number is negative?
• Can the absolute value of a number be negative?

Conclusion

Understanding absolute value helps in determining how far a number is from zero, which is a fundamental concept in mathematics.