To solve the expression \((-25 - (-20) - 1) + (1 - 4 - 1)\), let's evaluate it step-by-step.

### Step 1: Simplify each part of the expression inside the parentheses.

1. **First Parentheses**: \(-25 - (-20) - 1\)

\[
-25 - (-20) - 1 = -25 + 20 - 1
\]

Simplifying further:

\[
-25 + 20 = -5
\]

\[
-5 - 1 = -6
\]

So, the first part simplifies to \(-6\).

2. **Second Parentheses**: \(1 - 4 - 1\)

\[
1 - 4 - 1
\]

Simplifying from left to right:

\[
1 - 4 = -3
\]

\[
-3 - 1 = -4
\]

So, the second part simplifies to \(-4\).

### Step 2: Combine the simplified parts.

Now, add the results from both parts:

\[
-6 + (-4)
\]

\[
-6 - 4 = -10
\]

### Final Answer:

\[
\boxed{-10}
\]

Would you like a more detailed explanation, or do you have any other questions?

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Here are 5 related questions that expand on this concept:

1. How would the result change if the expression was \((-25 - (-20) + 1) + (1 - 4 - 1)\)?
2. What is the result of \((-30 - (-15) - 10) + (2 - 5 - 3)\)?
3. Can you simplify \((x - (-y) - z) + (a - b - c)\) for general \(x, y, z, a, b,\) and \(c\)?
4. How do the rules of subtraction and addition change when working with positive and negative integers?
5. What is the significance of the order of operations in solving mathematical expressions?

**Tip:** When dealing with multiple operations in an expression, always remember to follow the order of operations (PEMDAS/BODMAS).

Learn how to solve the arithmetic expression -25 - (-20) - 1 + 1 - 4 - 1 step-by-step. This problem involves integer arithmetic and order of operations (PEMDAS/BODMAS). Suitable for students in Grades 6-8.

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