Clara simplifies (8b - 4r) - (2b - r) and says the result is 6b - 5r. What error did Clara make? Options: 1. Clara incorrectly combined the b coefficients. The correctly simplified expression is 10b - 5r. 2. Clara incorrectly combined the r coefficients. The correctly simplified expression is 6b - 3r. 3. Clara incorrectly combined the r coefficients. The correctly simplified expression is 6b + 5r. 4. Clara incorrectly combined the b coefficients. The correctly simplified expression (incomplete).

To solve the problem and identify Clara's mistake, let's simplify the expression ( 8 b − 4 r ) − ( 2 b − r ) step by step:

Distribute the Negative Sign :
− ( 2 b − r ) becomes − 2 b + r .

Rewriting the Expression :
Substitute the distributed expression into the original: ( 8 b − 4 r ) − ( 2 b − r ) = 8 b − 4 r − 2 b + r

Combine Like Terms :
- Combine b terms: 8 b − 2 b = 6 b .
- Combine r terms: − 4 r + r = − 3 r .

Final Simplified Expression :
6 b − 3 r


Clara's error was in combining the coefficients of the r terms. Instead of adding − 4 r + r correctly to get − 3 r , she mistakenly got − 5 r .
Therefore, the correct answer is Option 2: Clara incorrectly combined the r coefficients. The correctly simplified expression is 6 b − 3 r .

Answered by IsabellaRoseDavis | 2025-07-21