Absolute values measure the distance of a number from zero on the number line, without considering direction. In simple terms, the absolute value of a number is always non-negative, as it represents how far the number is from zero.

### How Absolute Values Work:

1. **Positive Numbers:**
   - The absolute value of a positive number is the number itself.
   - Example: \(|5| = 5\).

2. **Negative Numbers:**
   - The absolute value of a negative number is the positive version of that number.
   - Example: \(|-5| = 5\).

3. **Zero:**
   - The absolute value of zero is zero.
   - Example: \(|0| = 0\).

### Mathematical Definition:
The absolute value of a number \(x\) is defined as:

\[
|x| = \begin{cases} 
x, & \text{if } x \geq 0 \\
-x, & \text{if } x < 0 
\end{cases}
\]

### Practical Example:
- If you have \(|-7| + |3|\), this simplifies to \(7 + 3 = 10\).

Absolute values are often used in distance calculations, solving equations, and inequalities.

Would you like to go into more detail or have any questions about this? 

### Follow-up Questions:
1. How are absolute values used in solving equations?
2. Can you explain how absolute values apply to real-life situations?
3. How do you solve absolute value inequalities?
4. What are the properties of absolute values?
5. How can absolute values be visualized on a number line?

**Tip:** Remember that the absolute value represents distance, so it’s always positive or zero.

Explore the concept of absolute values and their application in mathematics. Learn how to calculate the absolute value of numbers, including positive and negative integers, with clear examples and practical explanations. Suitable for Grades 6-8 students.

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