Let's break down the problems from the worksheet you've uploaded.

1. Inequalities: Use >, <, or = to compare the numbers.

• Compare $0$ and $| -10 |$:

  • $| -10 | = 10$ (the absolute value of -10 is 10).
  • Since $0 < 10$, the answer is $0 < | -10 |$.

• Compare $-100$ and $-200$:

  • $-100 > -200$ because -100 is closer to zero than -200.
  • The answer is $-100 > -200$.

2. Absolute Value & Opposites:

• The opposite of $17$ is $-17$.
• The opposite of $-6$ is $6$.

3. Calculate the absolute value:

• For $| 1 |$, the absolute value of 1 is $1$.

4. What is the key difference between finding the opposite and the absolute value of a number?

• Opposite: This means changing the sign of a number. For example, the opposite of 5 is -5, and the opposite of -5 is 5.
• Absolute value: This is the distance of a number from zero on the number line, regardless of direction. It’s always positive. For example, the absolute value of both 5 and -5 is 5.

Would you like more details on any part of this? Here are five related questions to expand your understanding:

1. What is the absolute value of a negative number, and why is it always positive?
2. How do you solve an inequality involving absolute values?
3. Can a number and its opposite ever be the same?
4. How would you graph absolute value on a number line?
5. What are some real-life applications of absolute values?

Tip: Absolute value is helpful when you want to know the "magnitude" of something, like distance, without considering direction!