In a coded arithmetic system, "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by". Using this code, what is the value of 81 x 9 + 10 – 6 ÷ 5?

Introduction / Context:
This is another operator coding problem. The four standard arithmetic signs are reassigned to different operations, and the coded expression 81 x 9 + 10 – 6 ÷ 5 must be interpreted accordingly. The final value depends on both correctly decoding the operators and then applying usual precedence rules for multiplication, division, addition and subtraction.

Given Data / Assumptions:

• "+" means "minus".
• "x" means "divided by".
• "÷" means "plus".
• "-" means "multiplied by".
• The coded expression is 81 x 9 + 10 – 6 ÷ 5.
• After decoding, we follow standard arithmetic precedence.

Concept / Approach:
We translate each occurrence of the coded symbols into the correct arithmetic operation. In this case, "x" becomes "/", "+" becomes "-", "–" becomes "*", and "÷" becomes "+". Then we evaluate the resulting expression, carrying out division and multiplication first, followed by addition and subtraction from left to right. Careful handling of negative values is essential.

Step-by-Step Solution:
Step 1: Decode the operators in 81 x 9 + 10 – 6 ÷ 5. "x" becomes "/", "+" becomes "-", "–" becomes "*", and "÷" becomes "+". Step 2: The decoded expression is 81 / 9 - 10 * 6 + 5. Step 3: Apply precedence. First evaluate 81 / 9 = 9. Step 4: Next compute 10 * 6 = 60. Step 5: Now the expression is 9 - 60 + 5. Step 6: Evaluate from left to right: 9 - 60 = -51. Step 7: Then -51 + 5 = -46.

Verification / Alternative check:
We can verify by recomputing the intermediate results. The division 81 / 9 gives 9, and the product 10 * 6 gives 60. Substituting these values yields 9 - 60 + 5, which clearly equals -51 + 5 = -46. This matches the option -46 exactly.

Why Other Options Are Wrong:
46 and 47 would require the overall sign or one intermediate sign to be reversed. -45 would require the difference between -51 and +5 to be miscalculated as -45 instead of -46. The option 0 would suggest complete cancellation, which does not occur here. Each of these wrong options corresponds to a typical small error in either decoding or arithmetic.

Common Pitfalls:
The most common errors are mixing up the new meanings of "+" and "-", or performing the addition before the multiplication and division are complete. Another frequent issue is sign mistakes when combining a positive and a negative number. Writing the decoded expression clearly and evaluating stepwise reduces these risks.

Final Answer:
Hence, after decoding the operators and simplifying, the value of 81 x 9 + 10 – 6 ÷ 5 is -46.