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

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

Part A: Margie made an error in Step 2. When subtracting a negative number, the operation is equivalent to adding the opposite. Therefore, (-5.38b) should be rewritten as (+5.38b).

Part B: To correctly write the expression in fewest terms, we would add like terms and combine the constants. The correct step 2 should be:

Step 2: -2.67b + 5.38b + 11 - 15

Now, we can add -2.67b and 5.38b:

2.71b + 11 - 15

Finally, let's combine the constants:

2.71b - 4

The corrected expression in fewest terms is 2.71b - 4.

Answer 2

Part A: The error made in the first step is when Margie added the terms -2.67b and -5.38b together. Instead of adding them, she should have subtracted -5.38b from -2.67b, which would be equal to (-2.67b) - (-5.38b).

Part B: To correctly write the expression in the fewest terms, we need to apply the correction from Part A.

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

Step 1: Distribution (distribute the negative sign across the second expression)

-2.67b + 11 - 5.38b + 15

Step 2: Combine like terms by adding or subtracting coefficients of similar variables

(-2.67b - 5.38b) + (11 + 15)

Step 3: Simplify further by performing the subtraction

(-2.67 - 5.38) b + (11 + 15)

Step 4: Simplify the coefficients

-7.05b + 26

The correct expression, written in fewest terms, is -7.05b + 26.

Answer 3

Part A: The mistake Margie made in the first step is when she switched the signs for the second term of the expression. Instead of subtracting (−5.38b), she mistakenly added (+5.38b) to the equation.

Part B: To correctly write the expression in the fewest terms and correct the error, we need to distribute the negative sign to both terms inside the parentheses before combining like terms. Here's the correct step-by-step approach:

Given: (−2.67b + 11) − (5.38b − 15)

Step 1: Distribute the negative sign:
−2.67b + 11 − 5.38b + 15

Step 2: Combine like terms:
(−2.67b − 5.38b) + (11 + 15)

Step 3: Simplify further:
−7.05b + 26

Therefore, the correct expression in the fewest terms is −7.05b + 26.