Solve 4376 + 3209 - 1784 + 97 = 3125 + x

### Concept & Formula To find the value of $x$, group all constants on one side of the equation using the standard rules of arithmetic operations (BODMAS). ### Step-by-Step Solution * **Step 1:** Simplify the left-hand side (LHS) of the equation: Add positive numbers first: $4376 + 3209 + 97 = 7682$ Subtract the negative number: $7682 - 1784 = 5898$ * **Step 2:** Equate the simplified LHS to the right-hand side (RHS): $$5898 = 3125 + x$$ * **Step 3:** Isolate $x$ by subtracting $3125$ from $5898$: $$x = 5898 - 3125$$ $$x = 2773$$ ### Exam Strategy & Shortcut **Unit Digit Trick:** Calculate the unit digit of both sides: LHS unit digit: $6 + 9 - 4 + 7 = 18 - 4 = 14 \rightarrow 4$ RHS expression: $5 + x \rightarrow$ must end in $4$. Therefore, the unit digit of $x$ must be $9$ (since $5 + 9 = 14$). Options (b) and (c) end in $3$, option (d) ends in $93$. Let's check the tens digits: LHS last two digits: $76 + 09 - 84 + 97 = 98$ RHS last two digits: $25 + x \rightarrow 98 - 25 = 73$. Thus, the answer must end in $73$, which leaves $2773$ as the correct choice. ### Common Pitfall * **Premature Transposition Error:** When shifting $3125$ to the other side, make sure its sign flips to negative. Accidentally adding it instead of subtracting is a common point of failure under exam stress. ### Final Answer **Therefore, the correct answer is 2773.**