In a certain code language, "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by". Using these rules, what is the value of 76 x 4 + 4 - 12 ÷ 37?

Introduction / Context:
This problem again redefines the standard arithmetic symbols. The challenge is to decode the expression properly and then evaluate it using standard operator precedence. It checks your ability to apply a coding key consistently and to handle mixed operations correctly.

Given Data / Assumptions:

• "+" means minus.
• "x" means divided by.
• "÷" means plus.
• "-" means multiplied by.
• Expression: 76 x 4 + 4 - 12 ÷ 37.
• Usual arithmetic precedence applies after decoding.

Concept / Approach:
As before, we begin by translating the coded expression into a normal arithmetic form. Once we have a standard expression with the usual symbols, we perform division and multiplication first, followed by addition and subtraction from left to right. Careful substitution is crucial, because a single incorrect replacement changes the whole result.

Step-by-Step Solution:
Step 1: Start with 76 x 4 + 4 - 12 ÷ 37.Step 2: Decode symbols: "x" means "÷", "+" means "minus", "-" means "multiplied by", and "÷" means "plus".Step 3: The decoded expression becomes: 76 ÷ 4 - 4 * 12 + 37.Step 4: Perform division and multiplication first: 76 ÷ 4 = 19, and 4 * 12 = 48.Step 5: Substitute into the expression: 19 - 48 + 37.Step 6: Now handle subtraction and addition from left to right: 19 - 48 = -29, then -29 + 37 = 8.

Verification / Alternative check:
Re reading the problem confirms that the coding scheme is identical to the one in the previous question, and the decoding step is applied consistently. Re computing each operation yields the same intermediate values 19 and 48 and the final result 8, so the answer is stable under re calculation.

Why Other Options Are Wrong:

• 9, 7, 3 and 11 would arise only if one or more symbols were mis decoded or if precedence was ignored.
• For example, treating "x" as multiplication instead of division or "+" as addition instead of minus would completely change the result.

Common Pitfalls:
The main traps are mixing up the substituted meanings of "+" and "-", and forgetting to apply precedence to the decoded expression. Another error is to treat the original sequence as if it were already in standard arithmetic, which it is not. Always write down the fully decoded expression and then compute carefully.

Final Answer:
After decoding and simplifying, the value of 76 x 4 + 4 - 12 ÷ 37 is 8.