Solving Equations with Absolute Value
📐 What is Absolute Value?
The absolute value of a number is its distance from zero on the number line, regardless of direction.
Formal Definition
For any real number $x$:
$$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$
In simple terms: absolute value strips away the negative sign (if there is one) and always returns a non-negative result.
Quick Examples:
- $|5| = 5$
- $|-5| = 5$
- $|0| = 0$
- $|-3.7| = 3.7$
Key Insight:
Since absolute value measures distance, the equation $|x| = 5$ asks: "What numbers are exactly 5 units from zero?"
Answer: $x = 5$ or $x = -5$
Interactive visualization — available in the full lesson