Select the new equation formed after collecting all variables on one side of the equal sign. (There is more than 1 correct answer.)

12(6x + 8) = x − 8

Responses

4 = -2x - 8
4 = -2x - 8

3x = x -12
3x = x -12

8 = -2x - 8
8 = -2x - 8

2x + 4 = -8
2x + 4 = -8

3x + 12 = x
3x + 12 = x

2x + 8 = 8

1 answer

To collect all variables on one side of the equation for the original equation \( 12(6x + 8) = x - 8 \), we first simplify the left side.

  1. Distributing \( 12 \) on the left side: \[ 12(6x + 8) = 72x + 96 \] So the equation becomes: \[ 72x + 96 = x - 8 \]

  2. Now subtract \( x \) from both sides: \[ 72x - x + 96 = -8 \] Which simplifies to: \[ 71x + 96 = -8 \]

  3. Next, subtract \( 96 \) from both sides: \[ 71x = -8 - 96 \] Which gives: \[ 71x = -104 \]

Now, we can rearrange the equation to have all variables and constants on one side. A few possible equations derived from this might look like:

  • \( 71x + 104 = 0 \)
  • \( -71x - 104 = 0 \)
  • \( 71x = -104 \)

Using your listed responses, let's verify:

  1. 4 = -2x - 8 → Not correct based on original equation.
  2. 3x = x - 12 → Not correct based on original simplified equation.
  3. 8 = -2x - 8 → Not correct based on original equation.
  4. 2x + 4 = -8 → Not directly relatable.
  5. 3x + 12 = x → Not correct based on original relation.
  6. 2x + 8 = 8 → Not directly correct.

The applicable forms I'm seeing in your options are not ideally matching the transition I see from the given initial form after simplification. Please check the possible variable manipulations, as none of these match my transformation exactly.