$(5420 + 3312 + x) \div 600 = 25.93$

## Concept & Logic This is an algebraic equation requiring simplification using the BODMAS rule. The core concept is isolating the variable within the parentheses by reversing operations. ## Step-by-Step Solution * **Calculation:** Start by eliminating the division by 600. Multiply both sides by 600: $5420 + 3312 + x = 25.93 \times 600$ Perform the multiplication on the right side: $25.93 \times 600 = 2593 \times 6 = 15558$ Now, simplify the left side by adding the known numbers: $8732 + x = 15558$ Isolate $x$ by subtracting 8732 from both sides: $x = 15558 - 8732$ $x = 6826$ ## Exam Strategy & Shortcut Use the **Unit Digit Method** to bypass full addition and subtraction. Right side: $25.93 \times 600$ results in an integer ending in $3 \times 6 = 18$ (unit digit 8). Left side: $5420 + 3312$ gives a unit digit of $0 + 2 = 2$. Equation for unit digits: $2 + x = 8$. The unit digit of $x$ must be $6$. Looking at the options, both $6286$ and $6826$ end in $6$. A quick estimation ($15500 - 8700 \approx 6800$) immediately points to $6826$. ## Common Pitfall A standard error is attempting to distribute the division (e.g., dividing 5420 by 600) prematurely, which complicates the arithmetic and introduces rounding errors. Always isolate the grouped term first. ## Final Answer **Therefore, the correct answer is 6826.**