Answer :

GinnyAnswer
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].

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