Which pair shows equivalent expressions?(1 point)

Question

Responses

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

−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

Answer 1

To determine which pairs of expressions are equivalent, we can simplify each equation and check their equality.

1. −2x−10 = −2(x+5)

   Simplifying the right side: \[ -2(x + 5) = -2x - 10 \] So, this is true: \[ -2x - 10 = -2x - 10 \] This pair shows equivalent expressions.

2. −2(x+5) = 2x−10

   Simplifying the left side: \[ -2(x + 5) = -2x - 10 \] This does not equal \(2x - 10\), so this pair is not equivalent.

3. 2x+10 = −2(x−5)

   Simplifying the right side: \[ -2(x - 5) = -2x + 10 \] This does not equal \(2x + 10\), so this pair is not equivalent.

4. −2(x−5) = −2x−10

   Simplifying the left side: \[ -2(x - 5) = -2x + 10 \] This does not equal \(-2x - 10\), so this pair is not equivalent.

Thus, the only pair that shows equivalent expressions is:

−2x−10 = −2(x+5).