Question Which pair shows equivalent expressions?(1 point) Responses −4(x+3)=4x−12 negative 4 times open paren x plus 3 close paren is equal to 4 x minus 12 4x+12=−4(x−3) 4 x plus 12 is equal to negative 4 times open paren x minus 3 close paren −4x−12=−4(x+3) negative 4 x minus 12 is equal to negative 4 times open paren x plus 3 close paren −4(x−3)=−4x−12

Answer 1

To determine which pair shows equivalent expressions, we can evaluate each option:

1. −4(x + 3) = 4x - 12: Expanding the left side:
   \(-4(x + 3) = -4x - 12\)
   The right side is \(4x - 12\).
   These are not equivalent.

2. 4x + 12 = −4(x − 3): Expanding the right side:
   \(-4(x - 3) = -4x + 12\)
   The left side is \(4x + 12\).
   These are not equivalent.

3. −4x − 12 = −4(x + 3): Expanding the right side:
   \(-4(x + 3) = -4x - 12\)
   Both sides are \(-4x - 12\).
   These are equivalent.

4. −4(x − 3) = −4x − 12: Expanding the left side:
   \(-4(x - 3) = -4x + 12\)
   The right side is \(-4x - 12\).
   These are not equivalent.

The equivalent expressions are found in option 3:
−4x − 12 = −4(x + 3).