Question

Margie's work for adding linear expressions is shown below. After checking her answer with the answer key, she solved it incorrectly. Given (-1.56b + 10) - (4.27b - 14), step 1: -1.56b + 10 -4.27b + 14, step 2: -1.56b - 4.27b + 10 + 14, step 3: (-1.56b - 4.27b) + (10 + 14), step 4: -5.83b + 24. 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.

Answer 1

Margie made an error in the first step by incorrectly combining the terms. To correct the error, we need to combine like terms and simplify the expression.

Step-by-step explanation:

In Margie's first step, she made an error by incorrectly combining the terms -1.56b and 10 to get -4.27b + 24. The correct combination should be -1.56b + 10 + 4.27b - 14.

To correctly write the expression in fewest terms, we can combine like terms. The coefficient of b in the resulting expression should be -1.56 - 4.27 = -5.83. The constant terms in the resulting expression should be 10 - 14 = -4.

Therefore, the correct expression in fewest terms is -5.83b - 4.