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Let's go through each part of your worksheet step by step.

### 1. **Inequalities:**
   You are asked to use `>`, `<`, or `=` to compare the numbers.

   - First comparison: \( 0 \) and \( | -10 | \).
     - The absolute value of \(-10\) is \(10\), so:
       \[
       0 < 10 \quad \text{or} \quad 0 < | -10 |
       \]

   - Second comparison: \( -100 \), \( 7 \), and \( -200 \).
     - Since \( -100 > -200 \) and \( 7 > -100 \), the correct comparison is:
       \[
       -100 < 7 > -200
       \]

### 2. **Absolute Value & Opposites:**

   - The opposite of \( 17 \) is \( -17 \).
   - The opposite of \( -6 \) is \( 6 \).

   Now, for calculating the absolute value:
   - \( | 8 | = 8 \), because the absolute value of a positive number is the number itself.

### 3. **Key Difference Between Opposite and Absolute Value:**
   - The opposite of a number refers to its sign being reversed (for example, the opposite of \( -5 \) is \( 5 \), and the opposite of \( 5 \) is \( -5 \)).
   - The absolute value of a number is its distance from zero, regardless of direction, and is always non-negative (for example, \( | -5 | = 5 \), and \( | 5 | = 5 \)).

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Would you like further details or have any questions about this?

Here are 5 related questions:
1. How do you compare absolute values of negative and positive numbers?
2. What is the absolute value of \(-200\)?
3. How do you calculate the opposite of a fraction, such as \( \frac{1}{2} \)?
4. If \( x > y \), how would you compare their absolute values?
5. Can a number have more than one opposite?

**Tip**: Remember, absolute values are always non-negative, while opposites can be either positive or negative.

Compare numbers and find opposites and absolute values of given numbers.

This problem teaches how to compare numbers using inequalities, find the opposites of numbers, and calculate absolute values. Explore key concepts like inequalities, absolute values, and opposites with a step-by-step solution. Suitable for Grades 5-7.

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