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 $| 5 | = 5$).

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.