In a certain coded system of arithmetic operations, the symbols are used as follows:\n\nThe minus sign (-) represents addition, the plus sign (+) represents multiplication, the multiplication sign (x) represents division and the division sign (÷) represents subtraction.\n\nUsing this code, find the value of the expression: 2 - 12 + 10 x 5 ÷ 12.

Introduction / Context:
This question again modifies the meanings of the familiar arithmetic symbols. The expression 2 - 12 + 10 x 5 ÷ 12 must be evaluated using these coded meanings. Your task is to decode each symbol correctly and then simplify the resulting ordinary arithmetic expression.

Given Data / Assumptions:

• - stands for addition.
• + stands for multiplication.
• x stands for division.
• ÷ stands for subtraction.
• Coded expression: 2 - 12 + 10 x 5 ÷ 12.
• We apply the normal precedence rules of arithmetic after decoding.

Concept / Approach:
The method is to translate the whole expression into one that uses the usual symbols but with the operations indicated by the code. Once rewritten, we simplify step by step, taking care to perform division and multiplication before addition and subtraction. The final result must match one of the answer options exactly.

Step-by-Step Solution:
Step 1: Replace - with +, because - now means addition. Step 2: Replace + with ×, because + now means multiplication. Step 3: Replace x with ÷, because x means division. Step 4: Replace ÷ with -, because ÷ means subtraction. Step 5: The coded expression 2 - 12 + 10 x 5 ÷ 12 becomes 2 + 12 × 10 ÷ 5 - 12. Step 6: Evaluate multiplication and division first. Step 7: Compute 12 × 10 = 120. Step 8: Then 120 ÷ 5 = 24. Step 9: Substitute back to get 2 + 24 - 12. Step 10: Now perform the additions and subtractions: 2 + 24 = 26 and 26 - 12 = 14.

Verification / Alternative check:
Rechecking, 12 × 10 is clearly 120, and 120 ÷ 5 is 24. Adding 2 gives 26, subtracting 12 gives 14. This is unique among the options, so our decoding and evaluation are correct.

Why Other Options Are Wrong:
The values 32, 8 and 4 would arise if we misinterpreted one or more symbols, for instance treating - as subtraction or + as addition. Another source of error is ignoring the precedence of multiplication and division, which changes intermediate results. Since the code and precedence are explicit, such alternatives are not acceptable.

Common Pitfalls:
Many students rush through the substitution step and end up mixing coded and normal meanings. Others treat all operations with the same priority and work strictly left to right. Writing down the fully decoded expression and then simplifying carefully step by step is the safest strategy for coded-operator problems.

Final Answer:
After decoding the symbols and simplifying correctly, the expression evaluates to 14, so option (d) is the correct answer.