In a certain code language, the symbols are redefined as follows: "-" represents "+", "+" represents "x", "x" represents "÷" and "÷" represents "-". Using these meanings, find the value of 3 ÷ 12 - 40 + 5 x 20.

Introduction / Context:
This is a coded-operations question where each arithmetic symbol has been reassigned a new meaning. We must decode the expression step by step, replacing each symbol with the correct real operation, and then evaluate the resulting arithmetic expression accurately.

Given Data / Assumptions:

• "-" means plus (+).
• "+" means multiplied by (×).
• "x" means divided by (÷).
• "÷" means minus (−).
• Expression: 3 ÷ 12 - 40 + 5 x 20.
• Standard operator precedence (× and ÷ before + and −) is used after decoding.

Concept / Approach:
We first translate each coded symbol to its true operation based on the mapping. Then we evaluate the transformed expression using normal arithmetic rules. It is important to substitute every operator correctly and to handle multiplication and division before addition and subtraction.

Step-by-Step Solution:
Start with 3 ÷ 12 - 40 + 5 x 20. Replace each symbol using the given mapping. "÷" becomes minus, so 3 ÷ 12 becomes 3 − 12. "-" becomes plus, so "− 40" becomes + 40. "+" becomes multiplied by, so "+ 5" becomes × 5. "x" becomes divided by, so "x 20" becomes ÷ 20. The decoded expression is: 3 − 12 + 40 × 5 ÷ 20. Apply operator precedence: compute × and ÷ first from left to right. 40 × 5 = 200. 200 ÷ 20 = 10. Now the expression becomes 3 − 12 + 10. Compute 3 − 12 = -9. Then -9 + 10 = 1.

Verification / Alternative check:
We can re-check quickly: only the final part 40 × 5 ÷ 20 is potentially tricky, but as long as multiplication is done before division and both are processed left to right, the result 10 is unambiguous. Substituting back confirms the final total is 1.

Why Other Options Are Wrong:
The values 42, 45 and 30 would result only if one or more symbols were misinterpreted or if the order of operations were applied incorrectly, such as doing addition before multiplication. Since our step-by-step decoding follows the defined meanings and correct precedence, these alternatives are incorrect.

Common Pitfalls:
Common mistakes include replacing only some of the operators, forgetting that plus and minus are also redefined, or evaluating strictly left to right without respect for precedence. Writing out the fully decoded expression clearly is the best way to avoid these traps.

Final Answer:
After decoding and evaluating, the expression 3 ÷ 12 - 40 + 5 x 20 equals 1.