Question

Select the two expressions that are equivalent.(2 points)
Responses

−7y−3x
negative 7 y minus 3 x

3x−7y
3 x minus 7 y

7y−3x
7 y minus 3 x

−7y+3x
negative 7 y plus 3 x

Answer 1

To determine which two expressions are equivalent, we need to analyze each one:

1. **−7y−3x** (negative 7 y minus 3 x)
2. **3x−7y** (3 x minus 7 y)
3. **7y−3x** (7 y minus 3 x)
4. **−7y+3x** (negative 7 y plus 3 x)

Let's look at the relationships:

1. The expression **−7y−3x** can be rearranged to **−3x−7y**, which means it is equivalent to **3x−7y** if we consider a change in sign and order (since addition is commutative).

2. The expression **3x−7y** is already simplified and can’t be adjusted further.

3. The expression **7y−3x** is not equivalent to the others because the signs and coefficients are different (it’s positive 7y and negative 3x).

4. The expression **−7y+3x** is not equivalent to the others either due to different signs for both terms compared to the first and the second.

Thus, the only two expressions that are equivalent when considering the properties of addition and the order of terms are:

- **−7y−3x**
- **3x−7y**

They reflect the same linear relationship but are represented in different forms.

Final answer: **−7y−3x** and **3x−7y**.