The expression 4[7+(w+5)]

Question

is manipulated to generate an equivalent expression. In which step, if any, does the first error occur?

4[7+(w+5)]

Step 1: 4[w+(7+5)]
Apply the Associative Property of Addition and add.
Step 2: 4[w+12]

Step 3: 4⋅w+12
Apply the Distributive Property.
(1 point)
Responses

Step 3
Step 3

Step 2
Step 2

no error
no error

Step 1

Answer 1

The first error occurs in Step 3.

Here’s why:

1. Step 1 changes the original expression \(4[7+(w+5)]\) to \(4[w+(7+5)]\) by using the Associative Property of Addition correctly. The expression \(7 + 5\) can indeed be regrouped.

2. Step 2 correctly simplifies \(7 + 5\) to \(12\), leading to \(4[w + 12]\).

3. Step 3 incorrectly applies the Distributive Property. The correct expansion should give \(4 \cdot w + 4 \cdot 12\) or \(4w + 48\), rather than \(4 \cdot w + 12\).

So the correct response is Step 3.