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. (6 points)
Part B: Explain how to correctly write the expression in fewest terms by correcting the error in Part A. Show all work. (6 points)
Part A: The first step where Margie made an error is in Step 2. She incorrectly combined (-3.12b) and (-4.36b) as (-3.12b + -4.36b) instead of (-3.12b - 4.36b).
Part B: To correctly write the expression in the fewest terms, we need to combine like terms.
Given: (-3.12b + 12) - (4.36b - 11)
Combining the like terms within the first set of parentheses, we have:
(-3.12b + 12) - 4.36b + 11
Now we can combine the like terms across the entire expression:
-3.12b - 4.36b + 12 + 11
Simplifying further:
-7.48b + 23