$10.0001 + 9.9999 - 8.9995 = $ $x$

### Concept & Strategy This problem evaluates mastery over the order of operations involving decimal addition and subtraction. Performing operations left-to-right ensures proper management of carrying and borrowing. ### Step-by-Step Solution * First, add the first two terms together by aligning their decimal points: * $10.0001$ * $+ \ 9.9999$ * Calculate the sum step-by-step from right to left: * $1 + 9 = 10 \rightarrow 0$, carry $1$ * $0 + 9 + 1 = 10 \rightarrow 0$, carry $1$ * $0 + 9 + 1 = 10 \rightarrow 0$, carry $1$ * $0 + 9 + 1 = 10 \rightarrow 0$, carry $1$ * $10 + 9 + 1 = 20$ * Intermediate Sum $= 20.0000$ * Next, subtract the third term from this intermediate sum: * $20.0000 - 8.9995$ * Perform standard column borrowing across the zeros: * $20.0000 - 8.9995 = 11.0005$ ### Exam Strategy & Shortcut **Complementary Visual Grouping:** Notice that $9.9999 - 8.9995 = 1.0004$. Now, simply add this result back to the first term: $10.0001 + 1.0004 = 11.0005$. By changing the order of calculation dynamically, you turn a multi-stage carry-and-borrow problem into a trivial mental addition step. ### Common Pitfall A common error lies in borrowing incorrectly from $20.0000$, resulting in values like $11.0001$ or forgetting to decrement the units place during continuous place-value borrowing. ### Final Answer **Therefore, the correct answer is $11.0005$.**