Let's solve the expression step-by-step, ensuring we follow the order of operations properly (parentheses/brackets, then addition and subtraction):
1. Innermost Parentheses: We first solve the innermost parentheses.
[tex]\[
4 + 4 = 8
\][/tex]
2. Substitute back and simplify: We substitute 8 back into the expression.
[tex]\[
17 - 8
\][/tex]
[tex]\[
17 - 8 = 9
\][/tex]
3. Next, simplify inside the brackets: The expression now becomes:
[tex]\[
9 + 3
\][/tex]
[tex]\[
9 + 3 = 12
\][/tex]
4. Then, move to the curly braces: Simplify inside the curly braces:
[tex]\[
4 - 12
\][/tex]
[tex]\[
4 - 12 = -8
\][/tex]
5. Include remaining operation inside the curly braces:
[tex]\[
-8 - 5
\][/tex]
[tex]\[
-8 - 5 = -13
\][/tex]
6. Final part of the expression: Now we consider the remaining part of the expression:
[tex]\[
6 + (-13)
\][/tex]
[tex]\[
6 - 13 = -7
\][/tex]
Therefore, the value of the expression [tex]\(6+\{4-[(17-(4+4)]+3\}-5\)[/tex] is [tex]\(-7\)[/tex].
