In a certain code language, "-" represents multiplication, "÷" represents addition, "+" represents division and "x" represents subtraction. Using this code, what is the value of 19 ÷ 2 - 35 + 10 x 6?

Introduction / Context:
This question presents another coded arithmetic expression. The familiar symbols "+", "-", "x" and "÷" are reassigned to different basic operations. The task is to decode each symbol, write the corresponding normal expression, and then evaluate that expression step by step using correct arithmetic precedence.

Given Data / Assumptions:

• "-" represents multiplication.
• "÷" represents addition.
• "+" represents division.
• "x" represents subtraction.
• The coded expression is 19 ÷ 2 - 35 + 10 x 6.
• Once decoded, we apply the usual precedence of operations (multiplication and division first, then addition and subtraction).

Concept / Approach:
We treat the coded symbols as direct replacements. That is, everywhere we see "÷" we read "+", everywhere we see "-" we read "*", "+" becomes "/", and "x" becomes "-". We then obtain a standard arithmetic expression that can be evaluated normally. Working symbol by symbol and maintaining the original order of numbers and parentheses keeps the logic clear and avoids mistakes.

Step-by-Step Solution:
Step 1: Apply the replacements to each operator in 19 ÷ 2 - 35 + 10 x 6. "÷" becomes "+", "-" becomes "*", "+" becomes "/", and "x" becomes "-". Step 2: The expression becomes 19 + 2 * 35 / 10 - 6. Step 3: Evaluate multiplication and division from left to right. First 2 * 35 = 70. Step 4: Then 70 / 10 = 7. Step 5: Now the expression is 19 + 7 - 6. Step 6: Evaluate addition and subtraction from left to right: 19 + 7 = 26. Step 7: Finally 26 - 6 = 20.

Verification / Alternative check:
We can independently recompute 2 * 35 / 10. Because multiplication and division have the same precedence, we perform them left to right: 2 * 35 = 70 and 70 / 10 = 7. Substituting this value back gives 19 + 7 - 6 = 20, confirming the result.

Why Other Options Are Wrong:
14, 32, 16 and 24 are values that can appear if one mistakenly treats "-" as subtraction, "x" as multiplication, or ignores left to right evaluation of multiplication and division. Such errors change one or more intermediate steps, leading to a different final number, but these numbers do not match the correctly decoded expression.

Common Pitfalls:
Many students forget that, after decoding, the expression must still follow conventional precedence rules. Some also try to decode and compute mentally at the same time, which increases the chance of mixing up the operators. A safer strategy is to rewrite the entire expression clearly with the true operations and only then carry out the arithmetic stepwise.

Final Answer:
Thus, the value of 19 ÷ 2 - 35 + 10 x 6 under the given coding is 20.