Opposite Absolute Value Equation

Question

When solving an absolute value equation, I know that I have to make two cases and make one of them the opposite of the original one. However, I am not sure on how I am supposed to negate it.

Here is an example:

| 4x + 8 | = 12 - This is my original equation and I know how to solve this.

However, for my second case, where would I put the negative sign?

Would it be: -| 4x + 8 | = 12

Or, would it be; | 4x + 8 | = -12

I have seen many videos on how to solve these and they each put the negative sign on a different side.

Is there a way I could know on which side to put it?

Thank you!

Answer 1

Answer 2

the second one. You should always consider that the absolute value is just the magnitude, so the sign stays with the right side.