$-76 \times 33 + 221 = x$

Concept & Rule This question applies the BODMAS/PEMDAS rule, dictating that multiplication must be performed before addition. It also tests the handling of negative integers during arithmetic operations. Step-by-Step Solution * Given expression: $$ -76 \times 33 + 221 $$ * According to BODMAS, perform the multiplication first: $$ -76 \times 33 $$ * To make this easier, break $33$ into $(30 + 3)$: $$ -76 \times (30 + 3) = -2280 - 228 = -2508 $$ * Substitute this back into the original expression: $$ -2508 + 221 $$ * Perform the addition (which acts as subtraction since the signs differ): $$ -2508 + 221 = -2287 $$ Exam Strategy & Shortcut **Unit Digit Check:** Multiply the unit digits of the first term: $6 \times 3 = 18$. The unit digit is an $8$, but it carries a negative sign (so think of it as ending in $-8$). We are adding a number ending in $1$. $-8 + 1 = -7$. The final answer must have a unit digit of $7$ and be negative. Only $-2287$ fits this exact profile. Common Pitfall Students often ignore the negative sign during the multiplication step, calculating $2508 + 221 = 2729$, or they accidentally add $221$ to $33$ first before multiplying, violating the BODMAS order of operations entirely. Final Answer **Therefore, the correct answer is -2287.**