232k views
0 votes
Margie's work for adding linear expressions is shown below. After checking her answer with the answer key, she solved it incorrectly.

Given (−3.12b + 12) − (4.36b − 11)
Step 1 −3.12b + 12 + (−4.36b) + 11
Step 2 −3.12b + −4.36b + 12 + 11
Step 3 (−3.12b + −4.36b) + (12 + 11)
Step 4 7.48b + 23


Part A: Identify and explain the first step where Margie made an error. (6 points)

Part B: Explain how to correctly write the expression in fewest terms by correcting the error in Part A. Show all work. (6 points)

Margie's work for adding linear expressions is shown below. After checking her answer-example-1

1 Answer

4 votes

Answer: Part A: Margie made an error in the first step of her work. The error lies in her attempt to simplify the expression (−3.12b + 12) − (4.36b − 11). She added the positive constant term 12 to the negative coefficient −4.36b, which resulted in −4.36b + 12. However, she should have subtracted 12 from −4.36b, which would have given her −4.36b − 12 instead. Part B: To correctly write the expression in the fewest terms, we need to correct the error in Part A. We start with the original expression (−3.12b + 12) − (4.36b − 11). To simplify it, we distribute the negative sign to each term inside the second set of parentheses, which gives us (−3.12b + 12) + (−4.36b + 11). Now, we can combine like terms. First, we add the −3.12b and −4.36b terms, which gives us −7.48b. Then, we add the 12 and 11 terms, which gives us 23. Therefore, the correct simplified expression is −7.48b +

User Roddy
by
7.9k points