If in a certain code language the symbol minus represents multiplication, the symbol division represents addition, the symbol plus represents division and the symbol x represents subtraction, then what is the value of 7 x 10 ÷ 30 - 2 + 6?

Introduction / Context:
Here we have another operator coding question where the usual mathematical symbols are assigned new meanings. The challenge is to translate the coded expression into a standard arithmetic expression and then evaluate it using normal rules for operator precedence. These problems build precision in handling symbol definitions and strengthen the discipline of doing calculations in the correct order.

Given Data / Assumptions:

• Minus represents multiplication.
• Division represents addition.
• Plus represents division.
• The symbol x represents subtraction.
• The coded expression is 7 x 10 ÷ 30 - 2 + 6.
• After decoding, standard arithmetic precedence applies: division and multiplication first, then addition and subtraction.

Concept / Approach:
We systematically replace each symbol in the expression with the operation it stands for. The expression 7 x 10 ÷ 30 - 2 + 6 becomes a new mixture of subtraction, addition, multiplication, and division in standard form. Then we evaluate this new expression by performing multiplication and division before addition and subtraction, moving from left to right where operations have equal precedence. Careful substitution is crucial to avoid mixing up the meanings of each coded symbol.

Step-by-Step Solution:
Step 1: Note the mapping of symbols to operations: x means subtraction, division means addition, minus means multiplication, and plus means division.Step 2: Rewrite the coded expression 7 x 10 ÷ 30 - 2 + 6 with real operations: 7 − 10 + 30 * 2 / 6.Step 3: Apply operator precedence. First evaluate the multiplication and division from left to right.Step 4: Compute 30 * 2 = 60.Step 5: Then compute 60 / 6 = 10.Step 6: Substitute these back. The expression is now 7 − 10 + 10.Step 7: Evaluate from left to right: 7 − 10 = −3, then −3 + 10 = 7.

Verification / Alternative check:
We can quickly redo the calculation for confidence. After decoding, there is exactly one multiplication and one division, which combine to a simple value of 10. Since subtraction and addition are both low precedence, we only need to ensure that we perform them in the correct left to right order. Recomputing in this way again returns the value 7, confirming that no arithmetic mistake has been made and the mapping was applied correctly.

Why Other Options Are Wrong:
The option 33 could appear if one treats the expression as 7 plus 10 plus 30 minus 2 plus 6, incorrectly ignoring the meanings of the coded symbols. The values 18 and 26 might result from partially correct decoding but an incorrect order of operations or missing the division step. The distractor 3 could come from misordering subtraction and addition. None of these equal the correctly evaluated value of 7 after decoding, so they are incorrect.

Common Pitfalls:
Students sometimes forget to replace every symbol and leave one or two in their original roles, which totally changes the result. Another common pitfall is to perform the operations strictly from left to right without respecting the higher precedence of multiplication and division. Writing out the translated expression clearly, then circling multiplication and division before doing any additions or subtractions, is a good habit to avoid these errors.

Final Answer:
After decoding the symbols and applying correct arithmetic precedence, the value of 7 x 10 ÷ 30 - 2 + 6 is 7.