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: -6.83b + 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 not distributing the negative sign. The correct step 1 is to distribute the negative sign to both terms inside the second set of parentheses.

Step-by-step explanation:

Margie made an error in the first step when simplifying the expression (-1.56b + 10) - (4.27b - 14). She incorrectly removed the parentheses without distributing the negative sign to both terms inside the second set of parentheses.

To correctly write the expression in fewest terms, you need to distribute the negative sign to both terms inside the second set of parentheses. The correct step 1 should be: -1.56b + 10 + (-4.27b) + 14.

Continuing with the correct steps, you can combine like terms to simplify the expression further.