In a certain code language, "÷" represents "+", "-" represents "x", "+" represents "÷" and "x" represents "-". Using this code, what is the value of 8 ÷ 14 - 20 + 5 x 2?

Introduction / Context:
This is another coded operations question where every arithmetic sign represents a different real operation. Once we decode all the operators in the expression 8 ÷ 14 - 20 + 5 x 2, we can evaluate the resulting normal expression using standard arithmetic rules to obtain the required answer.

Given Data / Assumptions:

• "÷" represents "+".
• "-" represents "x" (multiplication).
• "+" represents "÷" (division).
• "x" represents "-" (subtraction).
• The expression to evaluate is 8 ÷ 14 - 20 + 5 x 2.
• After decoding, we use normal precedence: multiplication and division before addition and subtraction.

Concept / Approach:
We systematically replace each symbol by the true operation it represents while keeping the numbers in the same order. This gives us a standard arithmetic expression. We then compute the result by first resolving all multiplication and division operations from left to right, and finally performing addition and subtraction in order from left to right.

Step-by-Step Solution:
Step 1: Apply the symbol mapping to the expression 8 ÷ 14 - 20 + 5 x 2. "÷" becomes "+", "-" becomes "*", "+" becomes "/", and "x" becomes "-". Step 2: The decoded expression is 8 + 14 * 20 / 5 - 2. Step 3: Carry out multiplication and division from left to right. First 14 * 20 = 280. Step 4: Then 280 / 5 = 56. Step 5: Now the expression reduces to 8 + 56 - 2. Step 6: Perform addition and subtraction from left to right: 8 + 56 = 64. Step 7: Finally 64 - 2 = 62.

Verification / Alternative check:
We can verify that no intermediate step was miscomputed: 14 * 20 is 280, 280 divided by 5 is 56, and 8 + 56 - 2 clearly equals 62. The sequence of operations respects precedence, so the result 62 is reliable.

Why Other Options Are Wrong:
46, 32, 20 and 14 arise from typical errors such as decoding one of the symbols incorrectly, ignoring the left to right evaluation of multiplication and division, or performing the operations in the wrong order. Any such misstep changes the intermediate values and leads to a different final answer than 62.

Common Pitfalls:
It is easy to mentally revert to the usual meanings of "+" and "÷" because they are so familiar. Another frequent mistake is treating all operations as if they had equal priority and evaluating purely left to right without honoring multiplication and division precedence. Writing down the decoded expression clearly and working slowly helps avoid these common errors.

Final Answer:
Therefore, under the given coding, the value of 8 ÷ 14 - 20 + 5 x 2 is 62.