Explanation:

This problem requires us to substitute the given new meanings for the mathematical operators and then evaluate the expression following the standard order of operations (BODMAS/PEMDAS). **Given Operator Transformations:** * `+` stands for `-` * `-` stands for `x` * `x` stands for `÷` * `÷` stands for `+` **Original Expression:** $14 - 3 + 10 \times 5 \div 5$ **Step 1: Substitute the operators with their new meanings.** * Replace `-` with `x` * Replace `+` with `-` * Replace `x` with `÷` * Replace `÷` with `+` \nThe expression becomes: $14 \times 3 - 10 \div 5 + 5$ **Step 2: Evaluate the new expression using the BODMAS/PEMDAS order of operations.** (Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)) 1. **Division:** Perform the division operation first. $10 \div 5 = 2$ The expression is now: $14 \times 3 - 2 + 5$ 2. **Multiplication:** Perform the multiplication operation next. $14 \times 3 = 42$ The expression is now: $42 - 2 + 5$ 3. **Addition and Subtraction (from left to right):** Perform these operations in the order they appear. * First, subtraction: $42 - 2 = 40$ * Next, addition: $40 + 5 = 45$ \nTherefore, the value of the expression is 45. \nLet's analyze why other options are incorrect based on the correct calculation: * **A. 65:** This would be obtained if multiplication and addition were prioritized differently or if errors in substitution occurred. For example, if $14 \times 3 + 10 \times 5 + 5$ was calculated as $42 + 50 + 5 = 97$, or if $14 \times 3 - 10 \div 5 + 5$ was incorrectly evaluated. * **B. 48:** This value is not reached through the correct order of operations or substitution. * **D. 40:** This is the result before the final addition of 5 ($42 - 2 = 40$). Missing the last step leads to this incorrect answer. \nThe only correct result following the rules is 45.