To solve the addition of [tex]\(-41\)[/tex] and [tex]\(-39\)[/tex], we follow these steps:
1. Understand the numbers to be added: We have two integers, [tex]\(-41\)[/tex] and [tex]\(-39\)[/tex], and both are negative.
2. Combine the absolute values: The absolute value of [tex]\(-41\)[/tex] is [tex]\(41\)[/tex] and the absolute value of [tex]\(-39\)[/tex] is [tex]\(39\)[/tex]. When adding two negative numbers, you add their absolute values:
[tex]\[
41 + 39 = 80
\][/tex]
3. Apply the negative sign to the result: Since both original numbers are negative, the result will also be negative.
Putting it all together:
[tex]\[
-41 + (-39) = -(41 + 39) = -80
\][/tex]
Thus, the final answer is:
[tex]\[
\boxed{-80}
\][/tex]
