In a certain code language, the minus sign represents multiplication, the division sign represents addition, the plus sign represents division and the symbol x represents subtraction. What is the value of the coded expression 5 - 6 + 30 x 8 ÷ 16 ?

Introduction / Context:
This code language problem reassigns new meanings to the standard arithmetic operators. We must translate each symbol back into its real operation and then evaluate the expression correctly. Because the expression involves all four operations, it is especially important to respect precedence rules while performing the calculation.

Given Data / Assumptions:

• The minus sign represents multiplication.
• The division sign represents addition.
• The plus sign represents division.
• The symbol x represents subtraction.
• The coded expression is 5 - 6 + 30 x 8 ÷ 16.
• Normal arithmetic precedence applies after decoding: multiplication and division before addition and subtraction.

Concept / Approach:
The plan is to decode each symbol correctly and rewrite the expression using ordinary plus, minus, multiplication and division signs. Once decoding is complete, we evaluate the resulting expression step by step, first carrying out the multiplication and division from left to right, then handling any addition and subtraction. Accurate translation of symbols and careful sequencing of operations are key to obtaining the correct answer.

Step-by-Step Solution:
Step 1: Interpret the minus sign as multiplication. So 5 - 6 becomes 5 × 6 in ordinary arithmetic. Step 2: Interpret the plus sign as division. So + 30 becomes ÷ 30. Step 3: Interpret the symbol x as subtraction. So 30 x 8 becomes 30 − 8. Step 4: Interpret the division sign as addition. So ÷ 16 becomes + 16. Step 5: Putting this all together, the decoded expression is 5 × 6 ÷ 30 − 8 + 16. Step 6: Evaluate multiplication and division first. Compute 5 × 6 = 30. Step 7: Then compute 30 ÷ 30 = 1. Step 8: The expression now simplifies to 1 − 8 + 16. Step 9: Perform subtraction and addition from left to right: 1 − 8 = −7. Step 10: Now add 16: −7 + 16 = 9. Step 11: Therefore, the value of the coded expression is 9.

Verification / Alternative check:
We can double check the arithmetic quickly. The key segment 5 × 6 ÷ 30 simplifies to 1, and the remainder of the expression is 1 − 8 + 16. Combining these gives 9 in a straightforward way. Since all symbol meanings have been applied consistently and the arithmetic is correct, the answer 9 is reliable.

Why Other Options Are Wrong:
The values 24, 36 and 37 arise only if one misinterprets the operator meanings or ignores precedence rules by, for example, adding or subtracting before completing the division. Because the decoded expression clearly collapses to 1 − 8 + 16, none of those other values can be obtained without some mistake in decoding or calculation.

Common Pitfalls:
A frequent error is to treat the symbol x as multiplication out of habit or to forget that plus has been repurposed as division. Another common trap is to evaluate 5 − 6 + 30 from left to right without first translating and then applying precedence. Writing a fully decoded version of the expression before computing is the best way to avoid such confusion.

Final Answer:
After decoding the symbols and evaluating the expression properly, the value of 5 - 6 + 30 x 8 ÷ 16 is 9.