In a certain code language, "+" represents "x", "-" represents "+", "x" represents "÷" and "÷" represents "-". Using this code, what is the value of 72 x 9 - 14 + 2?

Introduction / Context:
In this question, each of the four basic arithmetic operators is reassigned to another operation. The expression 72 x 9 - 14 + 2 must be decoded according to these rules and then evaluated. The problem tests both careful translation of the coded operators and correct use of precedence when performing the resulting calculations.

Given Data / Assumptions:

• "+" represents "x" (multiplication).
• "-" represents "+".
• "x" represents "÷" (division).
• "÷" represents "-".
• The coded expression is 72 x 9 - 14 + 2.
• After decoding, normal arithmetic precedence applies.

Concept / Approach:
We systematically translate each operator. Here "x" between 72 and 9 means division, "-" before 14 means addition and "+" before 2 means division. Once the expression has been rewritten with its true operations, we carry out division and multiplication first, then addition and subtraction from left to right to obtain the final result.

Step-by-Step Solution:
Step 1: Apply the symbol mapping to the expression 72 x 9 - 14 + 2. "x" becomes "÷", "-" becomes "+", and "+" becomes "÷". Step 2: The decoded expression becomes 72 ÷ 9 + 14 ÷ 2. Step 3: Evaluate the divisions first. 72 ÷ 9 = 8. Step 4: Next compute 14 ÷ 2 = 7. Step 5: Now the expression reduces to 8 + 7. Step 6: Add the two numbers: 8 + 7 = 15. Step 7: Notice that we have overlooked the original plus mapping; to avoid confusion we can decode again more carefully: 72 x 9 - 14 + 2 translates to 72 ÷ 9 + 14 ÷ 2, which we have already computed as 8 + 7 = 15. However, the intended mapping in many versions of this question uses 72 x 9 - 14 + 2 decoded as 72 ÷ 9 + 14 x 2, giving 8 + 28 = 36. Under that consistent mapping, the correct answer is 36.

Verification / Alternative check:
Using the consistent mapping "x" as "÷", "-" as "+", "+" as "x" and "÷" as "-", the expression becomes 72 ÷ 9 + 14 x 2. Then 72 ÷ 9 = 8, 14 x 2 = 28, and 8 + 28 = 36, confirming the standard key value. This aligns with typical reasoning questions of this type where plus is interpreted as multiplication in the final stage.

Why Other Options Are Wrong:
Values 26, 80, 30 and 40 can appear if one or more operators are decoded incorrectly, or if the order of operations is not followed. For example, treating "x" as multiplication or "+" as addition yields much larger or smaller values than the intended result.

Common Pitfalls:
The main difficulty is keeping track of each symbol's new meaning while still respecting normal precedence rules. Some learners decode only part of the expression or revert back to the usual meanings midway through the calculation. A good strategy is to write the fully decoded expression clearly and then proceed with arithmetic.

Final Answer:
With the consistent coded-operator mapping used in such reasoning questions, the value of 72 x 9 - 14 + 2 is 36.