mathematics

So if you look at the question x=9. All of it is positive. By this information you are looking for the possible ones that are positive. Another usage we can use is take out the slashes to read them normally.

So the first one is x = 9 so that's a keep

-x = 9 has a negative x so not it

If you remember the rules of positive and negatives, 2 negatives make a positive so it will read as x = 9. That's a keep

For the fourth, it has 3 negatives. The first to make the x positive but because there's not another negative it reads as x = -9. Not a keep

The fifth isn't it because of the -9

Not the sixth because of the -x

I'm not sure of the 7th because of the negatives can cross out to make them both possitive but at the same time it can read as -x= -9 on it's own.

So for your answer it is:

|x| = 9

–|–x| = 9

And maybe |–x| = –9 but I'd make sure

|x| = 9   →  l 9 l  =  9     OK

–|x| = 9 →   - l 9 l  =  -9     NO

–|–x| = 9  → - l -9 l  =  - 9   NO

–|–x| = –9   →  - l - 9 l  =  -9   OK

|x| = –9  →  l 9 l  =  9       NO

|–x| = 9  →    l -9 l   =  9   OK

|–x| = –9   →  l - 9 l  =  9   NO