Let's solve the given mathematical expression:

The expression is:

$\frac{12 - 10[(7 - 13) \div 2 - 2]}{2}$

Step 1: Simplify inside the parentheses

Start with $7 - 13$: $7 - 13 = -6$

Step 2: Division inside the brackets

$-6 \div 2 = -3$

Step 3: Subtract 2 from the result

$-3 - 2 = -5$

Now, the expression inside the brackets becomes $-5$.

Step 4: Multiply by 10

The updated expression is: $12 - 10(-5)$

$10 \times (-5) = -50$

Step 5: Simplify the numerator

$12 - (-50) = 12 + 50 = 62$

Step 6: Divide the result by 2

$\frac{62}{2} = 31$

Final Answer:

The value of the expression is:

$\boxed{31}$

Would you like further clarification on any step or additional examples?

Related Questions:

1. How do you simplify expressions with nested parentheses and brackets?
2. What is the order of operations (PEMDAS/BODMAS)?
3. How do you handle negative numbers in arithmetic operations?
4. What happens when multiplying a negative number by a positive one?
5. Can you solve more complex expressions with fractions and exponents?

Tip: Always work step-by-step in order (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).