Question

Which pair shows equivalent expressions?(1 point)Responses−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−12negative 4 times open paren x minus 3 close paren is equal to negative 4 x minus 124x+12=−4(x−3)4 x plus 12 is equal to negative 4 times open paren x minus 3 close paren−4(x+3)=4x−12

Answer 1

To determine which pair shows equivalent expressions, let's simplify each option.

1. Option 1: \(-4x - 12 = -4(x + 3)\)

   Simplifying the right side: \[ -4(x + 3) = -4x - 12 \] This equality holds: \[-4x - 12 = -4x - 12\] So these expressions are equivalent.

2. Option 2: \(-4(x - 3) = -4x - 12\)

   Simplifying the left side: \[ -4(x - 3) = -4x + 12 \] This does not match with \(-4x - 12\): \[-4x + 12 \neq -4x - 12\] Not equivalent.

3. Option 3: \(4x + 12 = -4(x - 3)\)

   Simplifying the right side: \[ -4(x - 3) = -4x + 12 \] Again, this does not match: \[4x + 12 \neq -4x + 12\] Not equivalent.

4. Option 4: \(-4(x + 3) = 4x - 12\)

   Simplifying the left side: \[ -4(x + 3) = -4x - 12 \] This does not match \(4x - 12\): \[-4x - 12 \neq 4x - 12\] Not equivalent.

From the evaluation above, the only pair that shows equivalent expressions is:

Option 1: \(-4x - 12 = -4(x + 3)\)