Let's solve the expression step-by-step:
1. Start by simplifying the innermost parentheses:
[tex]\[
8 - 6 - 7 + 1
\][/tex]
Calculate:
[tex]\[
8 - 6 = 2
\][/tex]
[tex]\[
2 - 7 = -5
\][/tex]
[tex]\[
-5 + 1 = -4
\][/tex]
So, [tex]\((8 - 6 - 7 + 1)\)[/tex] simplifies to [tex]\(-4\)[/tex].
2. Next, simplify the expression within the brackets:
[tex]\[
-5 + (-4)
\][/tex]
Calculate:
[tex]\[
-5 + (-4) = -9
\][/tex]
So, [tex]\([-5 + (-4)]\)[/tex] simplifies to [tex]\(-9\)[/tex].
3. Now simplify the expression outside the brackets:
[tex]\[
-10 - [-(-9)]
\][/tex]
Note: [tex]\(-(-9)\)[/tex] becomes [tex]\(9\)[/tex]. So, the expression is:
[tex]\[
-10 - 9
\][/tex]
Calculate:
[tex]\[
-10 - 9 = -19
\][/tex]
4. Simplify the remaining part of the expression:
[tex]\[
(-73 - 8)
\][/tex]
Calculate:
[tex]\[
-73 - 8 = -81
\][/tex]
5. Combine both parts of the simplified expression:
[tex]\[
-19 + (-81)
\][/tex]
Calculate:
[tex]\[
-19 + (-81) = -100
\][/tex]
Therefore, the simplified value of the expression is [tex]\(\boxed{-100}\)[/tex].
