To solve the expression [tex]\((2019 - (2000 - (10 - 9))) - (2000 - (10 - (9 - 2019)))\)[/tex], let's break it down step-by-step:
1. Evaluate the innermost parentheses:
[tex]\[
(10 - 9) = 1
\][/tex]
[tex]\[
(9 - 2019) = -2010
\][/tex]
2. Substitute these values back into the expression:
[tex]\[
(2019 - (2000 - 1)) - (2000 - (10 - (-2010)))
\][/tex]
3. Simplify the expressions inside the outer parentheses:
[tex]\[
2000 - 1 = 1999
\][/tex]
[tex]\[
10 - (-2010) = 10 + 2010 = 2020
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
(2019 - 1999) - (2000 - 2020)
\][/tex]
5. Simplify the remaining expressions:
[tex]\[
2019 - 1999 = 20
\][/tex]
[tex]\[
2000 - 2020 = -20
\][/tex]
6. Substitute these final values and complete the calculation:
[tex]\[
20 - (-20) = 20 + 20 = 40
\][/tex]
Therefore, the value of the expression [tex]\((2019 - (2000 - (10 - 9))) - (2000 - (10 - (9 - 2019)))\)[/tex] is [tex]\(\boxed{40}\)[/tex].
