Question

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

Answer 1

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.