If the symbols are redefined as follows: "×" means division, "−" means multiplication, "÷" means addition and "+" means subtraction, then what is the value of (3 − 15 ÷ 19) × 8 + 6 under these new meanings?

Introduction / Context:
This is another coded-operations problem in which arithmetic symbols do not carry their usual meanings. Instead, each symbol represents a different basic operation. To obtain the correct numerical value of the expression, we must first translate the entire expression into one using the standard operations, and then evaluate it carefully with the usual precedence rules.

Given Data / Assumptions:

• "×" means division.
• "−" means multiplication.
• "÷" means addition.
• "+" means subtraction.
• Expression: (3 − 15 ÷ 19) × 8 + 6.
• Brackets retain their usual role of forcing inner evaluation first.

Concept / Approach:
The bracketed part must be decoded and evaluated first. Every symbol is replaced according to the new definitions, not according to its usual meaning. After decoding, we obtain an expression entirely in terms of standard operations, which we can compute using the normal order of operations. Finally, we compare the result with the answer choices.

Step-by-Step Solution:
Decode "−" as multiplication and "÷" as addition inside the bracket. So 3 − 15 ÷ 19 becomes 3 × 15 + 19.Evaluate 3 × 15 = 45, then 45 + 19 = 64, so the bracket (3 − 15 ÷ 19) represents 64.Next, the outer "×" stands for division, so (3 − 15 ÷ 19) × 8 becomes 64 ÷ 8 = 8.Finally, the symbol "+" stands for subtraction, so 8 + 6 means 8 − 6, which equals 2.

Verification / Alternative check:
We can rewrite the fully decoded expression as (3 * 15 + 19) / 8 - 6 to make sure there is no confusion about the operations.Evaluating again: 3 * 15 = 45, 45 + 19 = 64, then 64 / 8 = 8, and 8 - 6 = 2, which confirms the answer.

Why Other Options Are Wrong:
A result of 8 would come from stopping the evaluation after dividing by 8 and forgetting that the final "+" actually means subtraction.Values like 4 or −1 generally arise if one of the symbols is misinterpreted, for example reading "+" as normal addition or treating "×" as multiplication instead of division.

Common Pitfalls:
The most common mistake is to apply the new meanings only partially, so that some symbols are decoded and others are still interpreted in the usual way.Another pitfall is to forget the precedence of operations after decoding, particularly when brackets and multiple operations such as addition and multiplication are combined.

Final Answer:
After decoding all symbols and following the correct order of operations, the value of the expression is 2.