In a coded arithmetic system, the meanings of the operators are changed as follows: the symbol + represents division, the symbol / represents subtraction, the symbol - represents multiplication, and the symbol x represents addition. Using this scheme, what is the value of the expression 24 + 8 / 26 x 6?

Introduction / Context:
Here we are given a numerical expression where the usual meanings of the arithmetic symbols have been changed. Instead of performing the operations implied by their standard meanings, we must interpret each symbol using the new code and then calculate the result following standard precedence rules. This type of question checks both careful reading of the symbol assignments and correct procedural execution of arithmetic once the expression has been decoded.

Given Data / Assumptions:

• In the code: + means division. • / means subtraction. • - means multiplication. • x means addition. • Expression given: 24 + 8 / 26 x 6. • After converting symbols to their real meanings, apply ordinary arithmetic precedence.

Concept / Approach:
The process has two stages. First, translate the expression by replacing each operator with its assigned real operation. Second, evaluate the translated expression carefully, respecting that multiplication and division are done before addition and subtraction. It is essential not to mix the coded meaning with the standard meaning during calculation, so we should write the decoded expression clearly on a separate line.

Step-by-Step Solution:
Step 1: Start with 24 + 8 / 26 x 6. Step 2: Replace + with division, so 24 + 8 becomes 24 ÷ 8. Step 3: Replace / with subtraction, so 8 / 26 becomes 8 − 26, but note that in the original sequence the slash sits between 8 and 26, and we have already accounted for 8 in the decoded structure as part of 24 ÷ 8. Interpreting as an expression with separate coded operators, the overall replacement produces 24 ÷ 8 − 26 + 6. Step 4: Replace x with addition, so 26 x 6 becomes 26 + 6, but in the decoded expression we already have subtraction and addition signs in place, leading to 24 ÷ 8 − 26 + 6. Step 5: The fully decoded expression to evaluate is 24 ÷ 8 − 26 + 6. Step 6: Apply precedence. First compute 24 ÷ 8 = 3. Step 7: Now handle addition and subtraction from left to right: 3 − 26 + 6. Step 8: Compute 3 − 26 = −23. Step 9: Then −23 + 6 = −17.

Verification / Alternative check:
As a check, note that the division produces a small positive value (3), then we subtract a large number (26) and finally add a smaller number (6). Intuitively this must lead to a negative result of moderate magnitude, which aligns with −17. None of the positive options, such as 12 or 21, can possibly be correct, and among the negative options only −17 matches the computed value.

Why Other Options Are Wrong:
Option −10 would arise from miscalculating either the division or one of the subsequent steps. Option −3 would come from incorrectly combining the subtraction and addition results. Option 12 ignores the fact that the large subtraction dominates and cannot produce a positive total. Option 21 similarly conflicts with both the sign and magnitude of the correct result.

Common Pitfalls:
Learners sometimes forget to rewrite the entire expression after decoding the operators, and instead try to convert and calculate simultaneously, which easily leads to errors. Another frequent error is to ignore operator precedence and perform operations strictly from left to right, which would produce a different and incorrect answer. Always decode first, then evaluate with proper order of operations.

Final Answer:
After applying the coded meanings of the operators and evaluating correctly, the value of the expression is −17.