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

Question

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

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.

In Step 2, she added -2.67b and 5.38b instead of subtracting them. She should have subtracted -5.38b instead of adding it.

Part B: To correctly write the expression in fewest terms, we need to subtract -5.38b instead of adding it.

Given: (-2.67b + 11) - (5.38b - 15)

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

Now, we can combine like terms:

-2.67b - 5.38b = -8.05b

11 + 15 = 26

Final result: -8.05b + 26

Answer 2

Part A: The error Margie made is in Step 2. She mistakenly combined the constant terms, 11 and 15, and overlooked the sign change when combining the coefficients of b.

Part B: To correctly write the expression in fewest terms, we need to perform the addition and subtraction correctly. Here's the correct step-by-step solution:

Given: (−2.67b + 11) − (5.38b − 15)

Step 1: −2.67b + 11 + (−5.38b) − 15
We need to distribute the negative sign to both terms inside the parentheses (-5.38b and -15) as we are subtracting them. This gives us:
-2.67b + 11 - 5.38b - 15.

Step 2: Combine like terms.
Combine the coefficients of b: -2.67b - 5.38b = -8.05b.
Combine the constants: 11 - 15 = -4.
The expression now becomes: -8.05b - 4.

So, the corrected expression, written in fewest terms, is -8.05b - 4.

Answer 3

Part A: Margie made an error in the first step. The error occurred when she added the positive number 15 to the expression (-5.38b). Instead of simply adding 15, she should have subtracted 15 since the expression (-5.38b) is preceded by a minus sign.

Part B: To correctly write the expression in the fewest terms, we need to correct the error made in Part A. Here's the correct step-by-step process:

Given: (-2.67b + 11) - (5.38b - 15)

Step 1: Distribute the negative sign to both terms inside the parentheses:
-2.67b + 11 - 5.38b + 15

Step 2: Combine like terms:
(-2.67b - 5.38b) + (11 + 15)
-8.05b + 26

Therefore, the correct expression in fewest terms is -8.05b + 26.