Understanding Absolute Value and Inequalities

📊 Understanding Absolute Value The absolute value of a number is its distance from zero

on the number line, regardless of direction. It's denoted by placing the number between two vertical

bars: . 🔢 Basic Definition and Examples For any real number :

If , then If , then Examples:

The absolute value essentially "removes the sign" from a number, always resulting

in a non-negative value. 📏 Connection to Distance The absolute value

has a crucial relationship with distance on the number line. The distance between two points with

coordinates and is given by: Why absolute value is necessary: Without it,