Symbol Substitution Logic

The problem requires substituting mathematical symbols based on a given code and then evaluating the expression using the standard order of operations (BODMAS/PEMDAS).

Symbol Mapping

First, let's establish the new meaning for each symbol as defined:

• '$+$' is replaced by '$-$' (subtraction).
• '$\div$' is replaced by '$+$' (addition).
• '$-$' is replaced by '$\times$' (multiplication).
• '$\times$' is replaced by '$\div$' (division).

Rewriting the Expression

The original expression is: $(8 + 2 - 19) - (4 + 27 \times 3)$

Now, apply the symbol substitutions to the entire expression:

• The '+' inside the first parenthesis becomes '-'.
• The '-' inside the first parenthesis becomes '$\times$'.
• The main '-' operator connecting the two parentheses becomes '$\times$'.
• The '+' inside the second parenthesis becomes '-'.
• The '$\times$' inside the second parenthesis becomes '$\div$'.

The transformed expression is: $(8 - 2 \times 19) \times (4 - 27 \div 3)$

Step-by-Step Evaluation

Evaluate the expression using the order of operations (Parentheses/Brackets, Orders/Exponents, Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right)).

1. Solve the first parenthesis: $(8 - 2 \times 19)$
   • Perform multiplication first: $2 \times 19 = 38$.
   • Perform subtraction: $8 - 38 = -30$.
2. Solve the second parenthesis: $(4 - 27 \div 3)$
   • Perform division first: $27 \div 3 = 9$.
   • Perform subtraction: $4 - 9 = -5$.
3. Perform the final operation: The expression is now $(-30) \times (-5)$.
   • Multiply the results: $(-30) \times (-5) = 150$.

Final Result

The value of the expression after applying the symbol substitutions and evaluating according to the order of operations is 150.