Certainly! Let's solve the mathematical expression step-by-step:
[tex]\[ 6 - \{ 9 - [9 + 2 - (6 - 3 + 20) - (7 - 2 + 15)] \} \][/tex]
1. Calculate the expressions inside the innermost parentheses:
[tex]\[ 6 - 3 + 20 = 23 \][/tex]
[tex]\[ 7 - 2 + 15 = 20 \][/tex]
2. Substitute these values back into the expression:
[tex]\[ 6 - \{ 9 - [9 + 2 - 23 - 20] \} \][/tex]
3. Simplify inside the brackets:
[tex]\[ 9 + 2 = 11 \][/tex]
[tex]\[ 11 - 23 = -12 \][/tex]
[tex]\[ -12 - 20 = -32 \][/tex]
4. Substitute back into the outer expression:
[tex]\[ 6 - \{ 9 - (-32) \} \][/tex]
5. Simplify the innermost braces:
[tex]\[ 9 - (-32) = 9 + 32 = 41 \][/tex]
6. Substitute back:
[tex]\[ 6 - 41 \][/tex]
7. Perform the final subtraction:
[tex]\[ 6 - 41 = -35 \][/tex]
Hence, the solution to the given expression is:
[tex]\[ \boxed{35} \][/tex]
