Question

is x=-|x| always sometimes or never

Answer 1

x=-x?

Answer 2

\(x\) can be either positive, negative, or zero.

\(|x|\) is always positive or zero, which means \(-|x|\) is always negative or zero.

Since both can be negative or zero, the answer definitely isn't never. What else can you eliminate?

Answer 3

Sometimes. x can equal any number, while -|x| can only be below zero.

Answer 4

what about |-x=-|x|

Answer 5

|-x|=-|x|

Answer 6

\(|\text{anything}|\) is always not negative (so it can be zero or positive).

\(|x|\) is always non-negative, but \(-|x|\) is always non-positive (zero or negative).

The fact that both *can* be zero means it's sometimes true.