To solve the expression [tex]\(5 - [6 - 2 - (1 - 8) - 3 + 0] + 5\)[/tex], we need to follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Solve inside the innermost parentheses first:
[tex]\[
1 - 8 = -7
\][/tex]
2. Substitute this result back into the expression:
[tex]\[
5 - [6 - 2 - (-7) - 3 + 0] + 5
\][/tex]
3. Simplify inside the brackets. Calculate each operation step by step:
[tex]\[
6 - 2 + 7 - 3 + 0
\][/tex]
First, perform the subtraction and addition within the brackets:
[tex]\[
6 - 2 = 4
\][/tex]
[tex]\[
4 + 7 = 11
\][/tex]
[tex]\[
11 - 3 = 8
\][/tex]
So, the expression then becomes:
[tex]\[
5 - [8] + 5
\][/tex]
4. Remove the brackets and simplify:
[tex]\[
5 - 8 + 5
\][/tex]
5. Perform the subtraction and addition from left to right:
[tex]\[
5 - 8 = -3
\][/tex]
[tex]\[
-3 + 5 = 2
\][/tex]
Therefore, the value of the expression [tex]\(5 - [6 - 2 - (1 - 8) - 3 + 0] + 5\)[/tex] is:
[tex]\[
2
\][/tex]
