In a certain code language, the symbol x represents addition, the division sign represents multiplication, the minus sign represents division and the plus sign represents subtraction. What is the value of the coded expression 15 x 4 ÷ 35 - 70 + 16 ?

Introduction / Context:
This arithmetic coding question replaces the usual plus, minus, multiplication and division signs with different symbols. The challenge is to decode the expression correctly and then apply standard arithmetic rules. The question focuses on careful symbol reading and correct precedence of operations, which are key skills in many competitive exams.

Given Data / Assumptions:

• The symbol x represents addition.
• The division sign represents multiplication.
• The minus sign represents division.
• The plus sign represents subtraction.
• The coded expression is 15 x 4 ÷ 35 - 70 + 16.
• We must interpret each symbol correctly and use normal operator precedence: multiplication and division before addition and subtraction.

Concept / Approach:
The first step is to rewrite the coded expression as a normal arithmetic expression using genuine plus, minus, multiplication and division symbols. Once decoding is complete, we then handle multiplication and division from left to right, followed by addition and subtraction from left to right. It is important not to mix up the symbol meanings during the translation process.

Step-by-Step Solution:
Step 1: Replace x with plus, because x represents addition. Thus 15 x 4 becomes 15 + 4. Step 2: Replace the division sign with multiplication. So ÷ 35 means × 35. Step 3: Replace the minus sign with division. So - 70 means ÷ 70. Step 4: Replace the plus sign with subtraction. So + 16 means − 16. Step 5: After decoding, the expression becomes 15 + 4 × 35 ÷ 70 − 16. Step 6: Apply precedence rules: evaluate 4 × 35 and 35 ÷ 70 before doing any addition or subtraction. Step 7: Compute 4 × 35 = 140. Step 8: Compute 140 ÷ 70 = 2. Step 9: Now the expression simplifies to 15 + 2 − 16. Step 10: Perform the remaining operations from left to right: 15 + 2 = 17. Step 11: Finally, 17 − 16 = 1.

Verification / Alternative check:
To verify, we can recheck the decoding and arithmetic quickly. The key part is confirming that only the segment 4 × 35 ÷ 70 is affected by multiplication and division first. That segment equals 2, and adding this to 15 and then subtracting 16 yields 1. Since every decoding step and arithmetic operation has been checked, the result 1 is reliable.

Why Other Options Are Wrong:
The values 15, 17 and 19 usually appear when candidates either treat x as multiplication out of habit or ignore operator precedence and work from left to right throughout. Some answers also come from misreading which symbol stands for which operation. Because only 1 is consistent with correct decoding and evaluation, the other options are clearly incorrect.

Common Pitfalls:
A very common error is to forget that the division sign has been reassigned to multiplication and that the minus sign has been reassigned to division. Another frequent mistake is to evaluate 15 + 4 first and then multiply, but this conflicts with the rule that multiplication and division must be handled before addition and subtraction. Writing down the translated expression in normal notation and then proceeding carefully helps avoid these issues.

Final Answer:
After decoding each symbol and applying standard arithmetic precedence, the value of the expression is 1.