$11.71 - 0.86 + 1.78 - 9.20 = $ $x$

### Concept & Logic Execute standard algebraic calculations safely by segregating positive rational numbers from negative ones, calculating their collective aggregates separately before completing the final subtraction. $$ \text{Result} = (\sum \text{Positive Terms}) - (\sum \text{Absolute Negative Terms}) $$ ### Step-by-Step Solution * Identify and cluster numbers based on their mathematical signs: * $\text{Positives} = 11.71, 1.78$ * $\text{Negatives} = 0.86, 9.20$ * Compute the total sum of the positive terms: * $11.71 + 1.78 = 13.49$ * Compute the total combined sum of the negative terms: * $0.86 + 9.20 = 10.06$ * Subtract the negative pool from the positive pool: * $x = 13.49 - 10.06 = 3.43$ ### Exam Strategy & Shortcut **Quick Fraction Scanning:** Group operations sequentially where simple: $11.71 + 1.78 = 13.49$. Subtract $9.20$ mentally first: $13.49 - 9.20 = 4.29$. Now finish by subtracting the final remaining piece: $4.29 - 0.86 = 3.43$. Breaking down continuous terms along clean mental boundaries eliminates computational overhead. ### Common Pitfall Mixing up columns or failing to carry across the decimal mark when adding $11.71$ and $1.78$ can result in choosing a distractor option like $2.43$ or $3.13$. ### Final Answer **Therefore, the correct answer is $3.43$.**