Question

Which of the following has no solution?



{x | x < 0} and {x | x > 0}

{x | x ≤ 0} and {x | x ≥ 0}

{x | x ≤ 0} or {x | x ≥ 0}

Answer 1

An absolute value is the distance from 0.
In this this case, x can only equal zero because there is no such thing as a "negative" zero.

Here is a normal example:
|x| = 3
This means that x = 3 and -3 because |-3| still equals 3

But, if the equation is equal to zero, it would look like this:

x = 0
x = -0

Since there is no "-0" (this equals 0), there is one solution, which is x = 0 :D