Let's solve the given expression step by step:
[tex]\[ 3 + \{4 + 8 - [5 - (-8 + 2 - 7 + 5) - 6] + (-9 - 7) + 8\} \][/tex]
Step 1: Evaluate the innermost expression:
[tex]\[ -8 + 2 - 7 + 5 \][/tex]
[tex]\[
-8 + 2 = -6
\][/tex]
[tex]\[
-6 - 7 = -13
\][/tex]
[tex]\[
-13 + 5 = -8
\][/tex]
So, [tex]\(-8 + 2 - 7 + 5 = -8\)[/tex].
Step 2: Substitute [tex]\(-8\)[/tex] into the expression:
[tex]\[ 3 + \{4 + 8 - [5 - (-8) - 6] + (-9 - 7) + 8\} \][/tex]
Since [tex]\(- (-8) = 8\)[/tex], the expression becomes:
[tex]\[ 3 + \{4 + 8 - [5 + 8 - 6] + (-9 - 7) + 8\} \][/tex]
Step 3: Simplify within the brackets:
[tex]\[ 5 + 8 - 6 \][/tex]
[tex]\[
5 + 8 = 13
\][/tex]
[tex]\[
13 - 6 = 7
\][/tex]
So, [tex]\(5 + 8 - 6 = 7\)[/tex].
Step 4: Substitute [tex]\(7\)[/tex] into the expression:
[tex]\[ 3 + \{4 + 8 - 7 + (-9 - 7) + 8\} \][/tex]
Step 5: Simplify inside the braces:
[tex]\[ -9 - 7 \][/tex]
[tex]\[
-9 - 7 = -16
\][/tex]
So, the expression now is:
[tex]\[ 3 + \{4 + 8 - 7 - 16 + 8\} \][/tex]
Step 6: Perform the arithmetic inside the braces:
[tex]\[ 4 + 8 = 12 \][/tex]
[tex]\[ 12 - 7 = 5 \][/tex]
[tex]\[ 5 - 16 = -11 \][/tex]
[tex]\[ -11 + 8 = -3 \][/tex]
So, \{4 + 8 - 7 + (-9 - 7) + 8\} simplifies to [tex]\(-3\)[/tex].
Step 7: Substitute [tex]\(-3\)[/tex] into the final expression:
[tex]\[ 3 + (-3) \][/tex]
Step 8: Perform the final arithmetic:
[tex]\[ 3 - 3 = 0 \][/tex]
Thus, the value of the given expression is [tex]\(0\)[/tex].
