In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 12 x 6 ÷ 5 + 4?

Introduction:
Once again we are given an arithmetic expression in which each familiar operator symbol has a new coded meaning. Our job is to interpret 12 x 6 ÷ 5 + 4 according to the redefined meanings of +, -, x and ÷, and then evaluate the resulting standard arithmetic expression. This problem checks both precise translation and correct use of operation precedence.

Given Data / Assumptions:
The symbol meanings are:
1) "+" represents multiplication.
2) "-" represents addition.
3) "x" represents division.
4) "÷" represents subtraction.
The coded expression we must evaluate is 12 x 6 ÷ 5 + 4. After decoding, we follow normal arithmetic rules where division and multiplication take precedence over addition and subtraction.

Concept / Approach:
The recommended approach is to perform the translation step carefully and only then proceed with the arithmetic. Each coded symbol is replaced by its actual operation, giving us a standard expression in terms of /, *, + and -. We then compute that expression step by step, ensuring that division and multiplication are processed before subtraction.

Step-by-Step Solution:
Step 1: Replace "x" with division: 12 x 6 becomes 12 / 6.Step 2: Replace "÷" with subtraction: "÷ 5" becomes - 5.Step 3: Replace "+" with multiplication: "+ 4" becomes * 4.Step 4: The decoded expression is therefore 12 / 6 - 5 * 4.Step 5: Apply operation precedence: first perform the division and multiplication from left to right.Step 6: Evaluate 12 / 6 = 2.Step 7: Evaluate 5 * 4 = 20.Step 8: Now substitute into the expression: 2 - 20.Step 9: Compute the result: 2 - 20 = -18.Step 10: Thus, the value of the coded expression is -18.

Verification / Alternative check:
We can restate the decoded expression in words: "twelve divided by six minus five multiplied by four". This is clearly 2 minus 20, which equals -18. There are no additional brackets in the original expression that would change the grouping, so the calculation is unambiguous once the operators are decoded.

Why Other Options Are Wrong:
The values 8, 42, 18, and 2 would arise only if we misinterpreted at least one symbol or ignored operator precedence. For example, interpreting "+" as addition instead of multiplication would change the result dramatically. Similarly, performing subtraction before multiplication would produce an incorrect intermediate value and an incorrect final answer.

Common Pitfalls:
A common error is to forget to change the meaning of the plus sign and still treat it as addition. Another frequent mistake is to perform operations in the written order rather than respecting the standard precedence of division and multiplication over addition and subtraction. A careful translation and stepwise, rule based evaluation keep these mistakes in check.

Final Answer:
When correctly decoded and evaluated, the expression has the value -18.