$-224 + (-314) \times (-9) = x$

Concept & Rule This problem tests the order of operations alongside negative integer arithmetic rules. Multiplication must be performed prior to addition. Crucially, the product of two negative numbers is always a positive number. Step-by-Step Solution * Given expression: $$ -224 + (-314) \times (-9) $$ * Step 1: According to BODMAS, evaluate the multiplication part first. $$ (-314) \times (-9) $$ Since multiplying two negatives yields a positive: $$ 314 \times 9 = 2826 $$ * Step 2: Substitute this result back into the original equation. $$ -224 + 2826 $$ * Step 3: Perform the addition. Since the signs are opposite, subtract the smaller absolute value from the larger one and keep the sign of the larger value. $$ 2826 - 224 = 2602 $$ Exam Strategy & Shortcut **Sign and Unit Digit Elimination:** You can solve this in seconds without full calculations. First, $(-314) \times (-9)$ will be a large positive number (around $+2700$). Subtracting $224$ will still leave a large positive number. This instantly eliminates options (a) and (b). Next, look at the unit digits. The product $4 \times 9 = 36$, so it ends in a $6$. The addition is essentially $(\text{number ending in } 6) - (\text{number ending in } 4)$. $6 - 4 = 2$. The final answer must be a positive number ending in $2$. Option (d) 2602 is the only logical choice. Common Pitfall The most common trap is a sign error during multiplication. Students hastily write $(-314) \times (-9) = -2826$, which leads to $-224 - 2826 = -3050$. Always double-check your integer sign rules before moving to the next step. Final Answer **Therefore, the correct answer is 2602.**