Question

Which pair shows equivalent expressions?(1 point)
Responses

−2(x+5)=2x−10
negative 2 times open paren x plus 5 close paren is equal to 2 x minus 10

2x+10=−2(x−5)
2 x plus 10 is equal to negative 2 times open paren x minus 5 close paren

−2(x−5)=−2x−10
negative 2 times open paren x minus 5 close paren is equal to negative 2 x minus 10

−2x−10=−2(x+5)

Answer 1

To determine which pair shows equivalent expressions, let's simplify each expression one by one.

1. **−2(x + 5) = 2x − 10**
- Left: −2(x + 5) = −2x - 10
- Right: 2x - 10
- These are **not equivalent**.

2. **2x + 10 = −2(x − 5)**
- Left: 2x + 10
- Right: −2(x − 5) = −2x + 10
- These are **not equivalent**.

3. **−2(x − 5) = −2x − 10**
- Left: −2(x − 5) = −2x + 10
- Right: −2x − 10
- These are **not equivalent**.

4. **−2x − 10 = −2(x + 5)**
- Left: −2x - 10
- Right: −2(x + 5) = −2x - 10
- These **are equivalent**.

Therefore, the pair that shows equivalent expressions is:

**−2x − 10 = −2(x + 5)**.