Question

(essay worth 4 points) (adding and subtracting linear expressions hc) 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)

Part a
a. Margie made an error in Step 1 by incorrectly distributing the subtraction inside the parentheses.
b. Margie made an error in Step 2 by combining like terms improperly.
c. Margie made an error in Step 3 by adding the terms inside parentheses incorrectly.
d. Margie made an error in Step 4 by incorrectly combining the coefficients.
Part b
a. The correct expression in fewest terms is \(2.71b + 26\).
b. To correct the error, the expression in fewest terms is \(2.71b - 4\).
c. The correct expression in fewest terms is \(-2.67b + 16.38\).
d. The correct expression in fewest terms is \(-2.71b + 26\).

Answer 1

Margie's error was in Step 1 where she did not distribute the subtraction sign correctly inside the parentheses. To correct this, distribute the negative sign properly, and combine like terms, resulting in the correct expression: −8.05b + 26.

Step-by-step explanation:

The student named Margie made an error while adding and subtracting linear expressions. The initial expressions given are (−2.67b + 11) − (5.38b − 15).

Part A: Identifying the Error

Margie's error occurred in Step 1 where she failed to distribute the subtraction sign inside the parentheses properly. This led to an incorrect sign in front of the 5.38b term when it should have been negative, as well as the incorrect sign in front of the constant term.

Part B: Correcting the Error

To correct the error and write the expression in the fewest terms:

1. First, distribute the negative correctly: −2.67b + 11 - 5.38b + 15.
2. Combine like terms by adding the coefficients of b: (−2.67b - 5.38b) + (11 + 15).
3. Simplify the expression: −8.05b + 26.