Question

Which pair shows equivalent expressions?(1 point)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−10negative 2 times open paren x plus 5 close paren is equal to 2 x minus 10−2(x−5)=−2x−10negative 2 times open paren x minus 5 close paren is equal to negative 2 x minus 102x+10=−2(x−5)

Answer 1

To determine which pair shows equivalent expressions, let's simplify each expression provided in the options:

1. −2x − 10 = −2(x + 5)

   • Left side: \(-2x - 10\)
   • Right side: \(-2(x + 5) = -2x - 10\)
   • These are equivalent.

2. −2(x + 5) = 2x − 10

   • Left side: \(-2(x + 5) = -2x - 10\)
   • Right side: \(2x - 10\)
   • These are not equivalent.

3. −2(x − 5) = −2x − 10

   • Left side: \(-2(x - 5) = -2x + 10\)
   • Right side: \(-2x - 10\)
   • These are not equivalent.

4. 2x + 10 = −2(x − 5)

   • Left side: \(2x + 10\)
   • Right side: \(-2(x - 5) = -2x + 10\)
   • These are not equivalent.

The only pair that shows equivalent expressions is:

−2x − 10 = −2(x + 5).