If the symbol x denotes \"added to\", the symbol ÷ denotes \"subtracted from\", the symbol + denotes \"divided by\" and the symbol – denotes \"multiplied by\", then what is the value of 14 x 12 – 16 ÷ 18 under these redefined operations?

Introduction / Context:
This is a classic operator-replacement question. The symbols x, ÷, +, and – no longer carry their usual arithmetic meanings. Instead, each symbol represents a different basic operation. We must carefully substitute the correct operations and then evaluate the expression using normal arithmetic precedence.

Given Data / Assumptions:

• x means \"added to\" (ordinary addition).
• ÷ means \"subtracted from\" (ordinary subtraction).
• + means \"divided by\" (ordinary division).
• – means \"multiplied by\" (ordinary multiplication).
• Expression: 14 x 12 – 16 ÷ 18.

Concept / Approach:
We translate each symbol into the operation it represents and then evaluate the resulting expression with standard precedence rules: multiplication and division first, then addition and subtraction, working from left to right as needed.

Step-by-Step Solution:
Step 1: Replace each symbol with its real meaning. x → +, – → ×, ÷ → −, + → ÷ (not used here). So 14 x 12 – 16 ÷ 18 becomes: 14 + 12 × 16 − 18. Step 2: Apply normal precedence: do the multiplication first. 12 × 16 = 192. Step 3: Now compute the remaining operations from left to right. 14 + 192 − 18. 14 + 192 = 206. 206 − 18 = 188.

Verification / Alternative check:
We can confirm there is only one multiplication and one subtraction. No hidden parentheses are implied, so performing multiplication before addition and subtraction is correct. Rechecking the symbol meanings shows we substituted each correctly, so 188 is reliable.

Why Other Options Are Wrong:
Values like 430, 180, and 168 would arise only if we misread one or more symbols (for example, treating x as multiplication or ÷ as division) or ignored precedence rules. Because the entire point of the question is the redefinition of operators, such interpretations are invalid.

Common Pitfalls:
The most common mistake is to mechanically apply the usual meaning of the symbols rather than the new meanings. Another pitfall is to evaluate from left to right without respecting multiplication precedence, which also gives an incorrect result.

Final Answer:
Under the redefined operations, the expression 14 x 12 – 16 ÷ 18 evaluates to 188.