Let's simplify the given expression step by step:

The expression is:

\[
 -(-6 + 4(2 - 5(4 - 3(4 - 3) + 2(7 - 3))) + 2) - 1
\]

**Step 1:** Simplify the innermost parentheses.

1. Simplify \( 4 - 3 \):

   \[
   4 - 3 = 1
   \]

2. Replace and continue simplifying:

   \[
   4 - 3(4 - 3) = 4 - 3 \times 1 = 4 - 3 = 1
   \]

3. Simplify \( 7 - 3 \):

   \[
   7 - 3 = 4
   \]

4. Multiply by 2:

   \[
   2 \times (7 - 3) = 2 \times 4 = 8
   \]

5. Combine with the earlier results:

   \[
   4 - 3(4 - 3) + 2(7 - 3) = 1 + 8 = 9
   \]

**Step 2:** Substitute back into the expression:

\[
5 \times (4 - 3(4 - 3) + 2(7 - 3)) = 5 \times 9 = 45
\]

\[
2 - 45 = -43
\]

**Step 3:** Multiply by 4:

\[
4 \times (-43) = -172
\]

**Step 4:** Continue with the expression:

\[
-6 + (-172) + 2 = -176
\]

**Step 5:** Simplify the expression with the negative sign:

\[
-(-176) - 1 = 176 - 1 = 175
\]

The final simplified value of the expression is:

\[
\boxed{175}
\]

Would you like a detailed explanation of any step? 

Here are some related questions to consider:

1. How do parentheses affect the order of operations?
2. How to simplify nested parentheses effectively?
3. What is the importance of the order of operations?
4. How does multiplication distribute over addition and subtraction?
5. How to handle negative signs in complex expressions?

**Tip:** Always simplify the innermost parentheses first to avoid errors with nested calculations!

Learn how to simplify the complex mathematical expression -(-6+4(2-5(4-3(4-3)+2(7-3)))+2)-1 step by step. This solution covers key concepts such as order of operations, handling nested parentheses, and applying the distributive property. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation