🎯 Goal
Understand absolute value as distance from zero on the number line and apply it to solve problems.
📖 Lesson Description
The absolute value of a number measures its distance from zero on the number line. Distance is always non-negative, so absolute value is never negative.
🔎 Definition
For any real number \(a\):
- \(|a| = a\) if \(a > 0\)
- \(|a| = -a\) if \(a < 0\)
Another way: \(|a|\) is the distance between \(a\) and 0.
📠Examples
- \(|7| = 7\)
- \(|-7| = 7\)
- \(|0| = 0\)
- \(|12 - 5| = |7| = 7\)
- \(|-3 + 8| = |5| = 5\)
âœï¸ Practice
- Evaluate: \(|-10|\)
- Evaluate: \(|15|\)
- Simplify: \(|-4 + 9|\)
- Fill in the blank: \(|\_\_| = 0\)
- On a number line, mark \(-6\) and \(6\). How are their absolute values related?