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.
Part B: Explain how to correctly write the expression in fewest terms by correcting the error in Part A. Show all work.
Part A: The error occurred in Step 1. Margie made a mistake when she distributed the negative sign to both terms inside the parentheses.
Part B: To correctly write the expression in fewest terms, we need to distribute the negative sign correctly.
The correct expression would be:
(−3.12b + 12) − (4.36b − 11)
= −3.12b + 12 + (-1)(4.36b) + (-1)(-11)
= -3.12b + 12 - 4.36b + 11
= (-3.12b - 4.36b) + (12 + 11)
= -7.48b + 23