Question

Peter is practicing how to apply the distributive property. In which example(s) did Peter NOT correctly apply the distributive property?
12(x-2)=12x-24,
3p-6=1/2(6p-12,
7(b+1)=7b+1
,-(w-2)=w+2, 8m+4=2(4m-2)

Answer 1

Let's examine each of the examples Peter used to see if he applied the distributive property correctly.

1. **Example: \( 12(x-2) = 12x - 24 \)**
To apply the distributive property here:
\( 12(x - 2) = 12 \cdot x - 12 \cdot 2 = 12x - 24 \)
This is correct.

2. **Example: \( 3p - 6 = \frac{1}{2}(6p - 12) \)**
Distributing on the right side:
\( \frac{1}{2}(6p - 12) = \frac{1}{2} \cdot 6p - \frac{1}{2} \cdot 12 = 3p - 6 \)
This is correct.

3. **Example: \( 7(b+1) = 7b + 1 \)**
Distributing on the left side:
\( 7(b + 1) = 7 \cdot b + 7 \cdot 1 = 7b + 7 \)
Here, Peter incorrectly wrote \( 7b + 1 \). This is not correct.

4. **Example: \(- (w - 2) = w + 2\)**
Distributing on the left side:
\(- (w - 2) = -w + 2 \)
Here, Peter wrote \( w + 2\), which is not correct.

5. **Example: \( 8m + 4 = 2(4m - 2) \)**
Distributing on the right side:
\( 2(4m - 2) = 2 \cdot 4m - 2 \cdot 2 = 8m - 4 \)
Here, Peter wrote \( 8m + 4\), which is also not correct.

### Summary
Peter did not correctly apply the distributive property in the examples:
- \( 7(b + 1) = 7b + 1 \)
- \(- (w - 2) = w + 2\)
- \( 8m + 4 = 2(4m - 2) \)

So, the incorrect examples are the third, fourth, and fifth.