In a certain code language, the operators are redefined as follows: "-" represents "×", "÷" represents "+", "+" represents "÷" and "x" represents "-". Using these meanings, what is the value of 160 + 8 x 30 ÷ 4 - 6 ?

Introduction / Context:
This is a coded arithmetic expression where each familiar operator symbol has been assigned a different arithmetic meaning. The expression 160 + 8 x 30 ÷ 4 - 6 must be evaluated under these new definitions. The question assesses whether you can accurately decode every occurrence of each operator and then evaluate the resulting standard expression using correct precedence rules.

Given Data / Assumptions:

• "-" represents "×" (multiplication).
• "÷" represents "+" (addition).
• "+" represents "÷" (division).
• "x" represents "-" (subtraction).
• Expression: 160 + 8 x 30 ÷ 4 - 6.
• After decoding, usual arithmetic precedence applies: division and multiplication before addition and subtraction.

Concept / Approach:
We should systematically replace each symbol in the given expression with the operation it now stands for. This creates a new expression written entirely in terms of the ordinary plus, minus, multiplication and division operators. Then we evaluate this new expression as usual, respecting precedence. It is important not to mix the original and redefined meanings during calculation, so writing down the decoded expression clearly is essential.

Step-by-Step Solution:
Step 1: Begin with the coded expression: 160 + 8 x 30 ÷ 4 - 6. Step 2: Apply the mapping of each operator. "+" represents "÷", so 160 + 8 becomes 160 ÷ 8. "x" represents "-", so 8 x 30 becomes 8 - 30. "÷" represents "+", so 30 ÷ 4 becomes 30 + 4. "-" represents "×", so - 6 becomes × 6. Step 3: Writing the full decoded expression, we have 160 ÷ 8 - 30 + 4 × 6. Step 4: Evaluate division and multiplication first. 160 ÷ 8 = 20. 4 × 6 = 24. Step 5: Substitute these results: 20 - 30 + 24. Step 6: Now carry out subtraction and addition from left to right. 20 - 30 = -10. -10 + 24 = 14.

Verification / Alternative check:
You can verify by re doing the decoding more slowly to confirm that each symbol has been replaced correctly: plus as division, x as subtraction, division as addition and minus as multiplication. Evaluating 160 ÷ 8 gives 20 and 4 × 6 gives 24, so the reduced expression must be 20 - 30 + 24. Because this simplifies neatly to 14 and this value appears among the answer choices, it is a strong indication that the decoding is correct. Alternative decodings that misassign any symbol do not match both the given mapping and the final value simultaneously.

Why Other Options Are Wrong:
Options 42, 5, 17 and 10 generally arise from computing with the wrong operation precedence or forgetting to recode one of the operators. For instance, treating x as multiplication or ÷ as division changes the structure dramatically and leads to a different answer. Because the properly decoded expression yields 14 and the mapping is clearly specified, all other numerical values must be rejected.

Common Pitfalls:
A typical pitfall is performing operations directly on the original expression without writing the decoded version. This invites confusion between old and new meanings. Another common error is to do addition and subtraction before resolving the multiplications and divisions in the decoded form. Carefully writing the full translated expression and underlining the division and multiplication operations before evaluating them is a good habit to avoid such mistakes.

Final Answer:
Using the given code for the operators, the value of 160 + 8 x 30 ÷ 4 - 6 is 14.