$3578 + 5729 - x \times 581 = 5821$

Concept & Formula This question requires basic algebraic manipulation and the application of the BODMAS/PEMDAS rule. You need to isolate the unknown variable by moving known quantities to one side of the equation. Step-by-Step Solution * The given equation is: $$3578 + 5729 - x \times 581 = 5821$$ * First, calculate the sum on the left side: $$3578 + 5729 = 9307$$ * Substitute this back into the equation: $$9307 - 581x = 5821$$ * Rearrange the equation to isolate the term with $x$: $$9307 - 5821 = 581x$$ * Perform the subtraction: $$3486 = 581x$$ * Solve for $x$: $$x = \frac{3486}{581}$$ $$x = 6$$ Exam Strategy & Shortcut Use the unit digit method to skip the final division. The subtraction $9307 - 5821$ ends in $6$ ($7 - 1 = 6$). So, $581 \times x$ must end in $6$. Since $581$ ends in $1$, the unit digit of $x$ must be $6$ because $1 \times 6 = 6$. Looking at the options, $6$ is the only choice that fits perfectly. Common Pitfall A frequent error is misapplying the order of operations, such as trying to subtract $581$ from the sum before multiplying by $x$, which violates BODMAS rules. Final Answer **Therefore, the correct answer is 6.**