To simplify the expression [tex]\(50 - \{15 - (20 - \overline{10 - 15})\}\)[/tex], let's break it down step by step.
1. Evaluate the innermost expression: [tex]\(\overline{10 - 15}\)[/tex]
[tex]\[
10 - 15 = -5
\][/tex]
2. Substitute [tex]\(-5\)[/tex] back into the expression:
[tex]\[
50 - \{15 - (20 - (-5))\}
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
20 - (-5) = 20 + 5 = 25
\][/tex]
4. Substitute [tex]\(25\)[/tex] back into the expression:
[tex]\[
50 - \{15 - 25\}
\][/tex]
5. Simplify the expression inside the braces:
[tex]\[
15 - 25 = -10
\][/tex]
6. Substitute [tex]\(-10\)[/tex] back into the expression:
[tex]\[
50 - (-10)
\][/tex]
7. Finally, simplify the overall expression:
[tex]\[
50 - (-10) = 50 + 10 = 60
\][/tex]
So, the simplified value of the expression is [tex]\(\boxed{60}\)[/tex].
