What value will replace the question mark in the following equation? $9587 - x = 7429 - 4358$

### Concept & Strategy When an equation contains operations on both sides, always simplify the side with purely known values first. Then, rearrange the equation to isolate the unknown variable, ensuring you manage the negative sign carefully. ### Step-by-Step Solution * **Given:** $9587 - x = 7429 - 4358$ * **Calculation:** First, simplify the right side of the equation by subtracting the values: $$ 7429 - 4358 = 3071 $$ * Substitute this back into the equation: $$ 9587 - x = 3071 $$ * Rearrange to isolate $x$. Add $x$ to both sides and subtract $3071$ from both sides: $$ x = 9587 - 3071 $$ * Perform the final subtraction: $$ x = 6516 $$ ### Exam Strategy & Shortcut Use the "Unit Digit" method for split-second option elimination. Calculate the unit digit of the right side: $9 - 8 = 1$. So, $9587 - x$ must end in $1$. Looking at the unit digit of the left side: $7 - (\text{unit digit of } x) = 1$. The unit digit of $x$ MUST be $6$. If only one option ends in 6, mark it and move on. ### Common Pitfall Students often fumble the algebraic signs during transposition. A common error is writing $x = 3071 - 9587$, resulting in a negative number, or mistakenly adding the numbers instead of subtracting. Always move the negative $x$ to make it positive. ### Final Answer Therefore, the correct answer is **6516**.