In a coded arithmetic system, "÷" denotes "multiplied by", "+" denotes "subtracted from", "x" denotes "added to" and "–" denotes "divided by". With these meanings, what is the value of 12 – 6 + 28 x 3 ÷ 9?

Introduction / Context:
This problem again uses coded operators. Each usual symbol is reassigned to a different arithmetic operation. The challenge is to translate the coded expression into a normal mathematical expression and then evaluate it carefully using the standard order of operations so that we obtain the correct final value.

Given Data / Assumptions:

• "÷" denotes "multiplied by".
• "+" denotes "subtracted from".
• "x" denotes "added to".
• "–" denotes "divided by".
• The given expression is 12 – 6 + 28 x 3 ÷ 9.
• After decoding, we use usual precedence: division and multiplication first, then addition and subtraction.

Concept / Approach:
A robust way to handle such questions is to perform a direct symbol replacement. Treat each coded symbol as if it were the new operator. So "–" is treated as "/", "+" as "-", "x" as "+", and "÷" as "*". We then write the decoded expression and evaluate it using standard rules without overthinking the descriptive phrases like "subtracted from" or "added to".

Step-by-Step Solution:
Step 1: Replace "–" with "/", "+" with "-", "x" with "+", and "÷" with "*". Step 2: The coded expression 12 – 6 + 28 x 3 ÷ 9 becomes 12 / 6 - 28 + 3 * 9. Step 3: Apply precedence. First handle division and multiplication: 12 / 6 = 2. Step 4: Next compute 3 * 9 = 27. Step 5: Now the expression is 2 - 28 + 27. Step 6: Evaluate from left to right: 2 - 28 = -26. Step 7: Then -26 + 27 = 1.

Verification / Alternative check:
We can quickly recompute: 12 / 6 = 2, 3 * 9 = 27, and 2 - 28 + 27 = (2 - 28) + 27 = -26 + 27 = 1. There are no ambiguities in precedence, so 1 is the only consistent value for the expression under the given coding rules.

Why Other Options Are Wrong:
The values -24, 0, -53 and 16 come from misplacing operations or ignoring the correct conversions. For instance, treating "÷" as division or "x" as multiplication yields different intermediate results. Other errors appear when addition and subtraction are done before resolving all multiplication and division. None of those incorrect approaches give the confirmed result of 1.

Common Pitfalls:
Candidates sometimes try to interpret the language "subtracted from" by reversing operands, which complicates the problem. Here, a simpler and completely consistent method is to treat each symbol as a direct replacement operator and then follow strict precedence. Another common mistake is to rush through the evaluation and commit sign errors when combining negative and positive terms.

Final Answer:
Therefore, after decoding the operators and evaluating correctly, the value of 12 – 6 + 28 x 3 ÷ 9 is 1.