Let's solve problems 19 and 21 from the provided image:

Problem 19:

$-2 - [(-6)] + | -5 |$

Step-by-step Solution:

1. Evaluate the expression inside the brackets: $-(-6) = 6$
2. Substitute back into the expression: $-2 - 6 + | -5 |$
3. Calculate the absolute value: $| -5 | = 5$
4. Combine the values: $-2 - 6 + 5 = -2 - 1 = -3$

Final Answer for 19: $-3$

Problem 21:

$| -2 - 5 | - (-7) - (-4)$

Step-by-step Solution:

1. Evaluate inside the absolute value: $-2 - 5 = -7$
2. Find the absolute value: $| -7 | = 7$
3. Evaluate the negative terms: $-(-7) = 7 \quad \text{and} \quad -(-4) = 4$
4. Combine all terms: $7 + 7 + 4 = 18$

Final Answer for 21: $18$

Would you like more details on any step, or do you have any other questions?

Here are some related questions for practice:

1. How do you evaluate an expression with nested absolute values?
2. What is the process to simplify an expression with multiple negative signs?
3. How does the order of operations affect solving these expressions?
4. Can absolute values be negative? Why or why not?
5. How do brackets differ from absolute values in mathematical expressions?

Tip: When solving expressions, always handle brackets and absolute values first before performing other operations.