Question

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

Given (−2.67b + 11) − (5.38b − 15)
Step 1 −2.67b + 11 + (−5.38b) + 15
Step 2 −2.67b + 5.38b + 11 + 15
Step 3 (−2.67b + 5.38b) + (11 + 15)
Step 4 2.71b + 26


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 1

Given (-2.67b+11)-(5.38b-15)
Step 1 change the second () the opp signs because a - is in front of the second () so in Step 1 this is shown correctly
Step 2 is where the mistake is because in step 1 (-5.38) is shown in brackets and a plus in front of () does not change the signs to solve the bracket you just leave it in brackets and simplify as much as possible
Step 2 should be
-2.67b+11-5.38b+15
Step 3 is
-8.05b+26

Answer 2

Part A: Margie made an error in the first step when she added the expression (-5.38b) and 15. She should have subtracted 5.38b from 11, rather than adding it.

Part B: To correctly write the expression in the fewest terms, we need to combine like terms. Let's correct the error in Part A and simplify the expression:

Given expression: (-2.67b + 11) - (5.38b - 15)

Step 1: (-2.67b + 11) - (5.38b - 15)

Step 2: -2.67b + 11 - 5.38b + 15 (Corrected Step)

Step 3: (-2.67b - 5.38b) + (11 + 15)

Step 4: -8.05b + 26

So, the correct expression in fewest terms is -8.05b + 26.