In a certain code language, the symbols are redefined so that "-" represents "+", "+" represents "x", "x" represents "÷" and "÷" represents "-". Using these rules, what is the value of 9 - 18 + 35 x 10 ÷ 30?

Introduction / Context:
This coding decoding problem changes the meanings of the arithmetic operators. You must carefully translate each symbol into its true arithmetic role and then evaluate the resulting expression. The challenge lies in not confusing the original printed symbol with the operation it actually represents under the coding scheme.

Given Data / Assumptions:

• "-" represents "+".
• "+" represents "x" (multiplication).
• "x" represents "÷" (division).
• "÷" represents "-".
• Coded expression: 9 - 18 + 35 x 10 ÷ 30.
• Standard arithmetic precedence applies after decoding.

Concept / Approach:
First decode the expression by replacing every coded symbol with the real operation it stands for. Second, evaluate the new expression using normal rules: perform all multiplication and division operations before addition and subtraction. Writing the decoded expression separately helps avoid mistakes caused by mentally juggling the meanings.

Step-by-Step Solution:
Step 1: Start with 9 - 18 + 35 x 10 ÷ 30.Step 2: Replace each symbol: "-" becomes "+", "+" becomes "x", "x" becomes "÷", and "÷" becomes "-".Step 3: The decoded expression becomes: 9 + 18 x 35 ÷ 10 - 30.Step 4: Evaluate multiplication and division from left to right: 18 x 35 = 630, then 630 ÷ 10 = 63.Step 5: Substitute back: 9 + 63 - 30.Step 6: Now handle addition and subtraction: 9 + 63 = 72 and 72 - 30 = 42.

Verification / Alternative check:
Re check the substitution: no "+" or "-" remains undecoded, and there is exactly one multiplication and one division inside the middle part 18 x 35 ÷ 10. Repeating the calculations confirms that the middle block evaluates to 63 and the overall expression to 42. So our answer is consistent and does not depend on any unusual convention.

Why Other Options Are Wrong:

• 40, 44, 39 and 41 arise from common errors such as decoding only some symbols or doing operations strictly left to right.
• Any option different from 42 indicates at least one mistake either in the substitution step or in handling precedence.

Common Pitfalls:
Many candidates accidentally treat the symbols according to their usual meaning rather than their coded meaning. Others forget that after decoding, multiplication and division must be evaluated before addition and subtraction. Writing down the decoded expression clearly is the simplest way to keep the operations straight in your mind.

Final Answer:
After decoding the operators and simplifying, the value of the expression is 42.