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

Question

Given (−2.67b + 11) − (5.38b − 15)
Step 1 −2.67b + 11 + (−5.38b) + 15
Step 2 −2.67b + 5.38b + 11 + 15
Step 3 (−2.67b + 5.38b) + (11 + 15)
Step 4 2.71b + 26

Part A: Identify and explain the first step where Margie made an error. (2 points)

Part B: Explain how to correctly write the expression in fewest terms by correcting the error in Part A. Show all work. (2 points)

Answer 1

Part A: Margie made an error in Step 2. When subtracting a negative number, the operation is equivalent to adding the opposite. Therefore, (-5.38b) should be rewritten as (+5.38b).

Part B: To correctly write the expression in fewest terms, we would add like terms and combine the constants. The correct step 2 should be:

Step 2: -2.67b + 5.38b + 11 - 15

Now, we can add -2.67b and 5.38b:

2.71b + 11 - 15

Finally, let's combine the constants:

2.71b - 4

The corrected expression in fewest terms is 2.71b - 4.