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


Given (−4.23b + 13) − (5.47b − 12)
Step 1 −4.23b + 13 + (−5.47b) + 12
Step 2 −4.23b + −5.47b + 13 + 12
Step 3 (−4.23b + −5.47b) + (13 + 12)
Step 4 9.7b + 25


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 :

Using addition of integers, it is found that:

A. Margie's first error was in Step 3, as when two negative terms are added, the signal remains negative and the quantities are added.

B. The simplified expression is given as follows: -9.7b + 25.

How does the addition of integers works?

If the two integers have the same signal, the addition is simple, as we just keep the signal, either negative or positive, and add the absolute amounts(amounts without the signal).

With different signals, it is more difficult, we have to verify which term has the higher absolute value, then we keep the signal of this term, and add them.

Hence, the addition of -4.23b and -5.47b, where Margie's commits her first error, falls in the first case, as both are negative, hence:

-4.23b - 5.47b = -(4.23b + 5.47b) = -9.7b.

The addition of 13 and 12 is done correctly, hence the term 25 is part of the solution of the expression.

Hence:

A. Margie's first error was in Step 3, as when two negative terms are added, the signal remains negative and the quantities are added.

B. The simplified expression is given as follows: -9.7b + 25.

More can be learned about the addition of integers at https://brainly.com/question/17695139

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