To solve the expression [tex]\(6 - [4 - 3(4 - 2)] - \{7 - 5[4 - 2(7 - 1)]\}\)[/tex] step-by-step, let's carefully work through each component.
1. Start with the innermost parentheses:
[tex]\[
4 - 2
\][/tex]
which equals:
[tex]\[
2
\][/tex]
Another inner expression:
[tex]\[
7 - 1
\][/tex]
which equals:
[tex]\[
6
\][/tex]
2. Next, complete the multiplications within the brackets and braces:
Substituting back in:
[tex]\[
3(2)
\][/tex]
which equals:
[tex]\[
6
\][/tex]
Another multiplication:
[tex]\[
2(6)
\][/tex]
which equals:
[tex]\[
12
\][/tex]
3. Now, substitute these results back into the expressions within the brackets and braces:
[tex]\[
4 - 6
\][/tex]
which equals:
[tex]\[
-2
\][/tex]
Another calculation:
[tex]\[
4 - 12
\][/tex]
which equals:
[tex]\[
-8
\][/tex]
4. Evaluate the expression within the braces:
Multiplying by 5:
[tex]\[
5(-8)
\][/tex]
which equals:
[tex]\[
-40
\][/tex]
5. Now, compute within the braces again:
[tex]\[
7 - (-40)
\][/tex]
which equals:
[tex]\[
47
\][/tex]
6. Substitute results back into the original brackets and braces operations:
Simplifying the expression within the outermost brackets:
[tex]\[
-2 - 47
\][/tex]
which equals:
[tex]\[
-49
\][/tex]
7. Finally, compute the outermost expression:
[tex]\[
6 - (-49)
\][/tex]
which equals:
[tex]\[
55
\][/tex]
Therefore, the solution to the expression [tex]\(6 - [4 - 3(4 - 2)] - \{7 - 5[4 - 2(7 - 1)]\}\)[/tex] is [tex]\(55\)[/tex].
