Let's address the tasks in the worksheet:

1. Inequalities Section:

For comparing the absolute values and other numbers:

• $|3|$ versus $7$ versus $|-1|$:

  • $|3| = 3$
  • $|-1| = 1$
  • Thus, $3 < 7$ and $7 > 1$.
  • The correct inequality is: $|3| < 7 > |-1|$.

• $|-3|$ versus $-4$:

  • $|-3| = 3$
  • Thus, $3 > -4$.
  • The correct inequality is: $|-3| > -4$.

2. Absolute Value & Opposites Section:

• Opposite of $0$:

  • The opposite of $0$ is $0$.

• Opposite of $-12$:

  • The opposite of $-12$ is $12$.

3. Calculate Absolute Value:

• $|-10.5|$:
  • The absolute value of $-10.5$ is $10.5$.

Would you like more detailed explanations on any part? Here are some related questions you might explore:

1. What are the properties of absolute values?
2. How do opposites of numbers relate to their signs?
3. When comparing absolute values, what should be considered?
4. How do absolute values affect inequality relations?
5. What happens to inequalities when multiplying or dividing by negative numbers?

Tip: Always remember that the absolute value of a number is its distance from zero on the number line, regardless of direction.