Certainly! Let's break down and solve the expression step by step:
Given expression:
[tex]\[ -2 - \{-3 - [6 + 8 + (-3 - 7 - 1)] \} \][/tex]
Step-by-Step Solution:
1. Innermost Parentheses:
First, solve the expression inside the innermost parentheses [tex]\( (-3 - 7 - 1) \)[/tex]:
[tex]\[ -3 - 7 - 1 = -11 \][/tex]
2. Next Level Parentheses:
Replace [tex]\( (-3 - 7 - 1) \)[/tex] with its calculated value (-11) inside the brackets:
[tex]\[ 6 + 8 + (-11) \][/tex]
3. Simplify the resulting sum inside the brackets:
[tex]\[ 6 + 8 - 11 = 3 \][/tex]
4. Outer Brackets:
Replace [tex]\( [6 + 8 + (-11)] \)[/tex] with its calculated value (3):
[tex]\[ -3 - 3 \][/tex]
5. Simplify the resulting difference inside the curly braces:
[tex]\[ -3 - 3 = -6 \][/tex]
6. Curly Braces:
Replace [tex]\( \{-3 - [6 + 8 + (-11)]\} \)[/tex] with its calculated value (-6):
[tex]\[ -2 - (-6) \][/tex]
7. Finally, simplify the overall expression:
[tex]\[ -2 - (-6) = -2 + 6 = 4 \][/tex]
Thus, the value of the given expression is:
[tex]\[ \boxed{4} \][/tex]
