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.

1. First expression: \(-2(x + 5)\) \[ = -2x - 10 \] So, \(-2(x + 5) = -2x - 10\)

   Comparing with: \(2x - 10\) → This is not equivalent.

2. Second expression: \(2x + 10\) \[ = -2(x - 5) \] \[ = -2x + 10 \] So, \(2x + 10 \neq -2(x - 5)\)

3. Third expression: \(-2(x - 5)\) \[ = -2x + 10 \] Comparing with: \(-2x - 10\) → This is not equivalent.

4. Fourth expression: \(-2x - 10\) Comparing with: \(-2(x + 5)\) \[ = -2x - 10 \]

Based on the simplifications, the equivalent expressions are: \[ -2(x + 5) = -2x - 10 \] and \(-2x - 10 = -2(x + 5)\)

Thus, the correct answer is: \(-2(x + 5) = -2x - 10\) and \(-2x - 10 = -2(x + 5)\).