Question

Which of the following is the set of all real number x such that x-2 < x-4?

Answer 1

If you subtract x from both sides, then you go from

x-2 < x-4

to

-2 < -4

which is a false statement. The value -2 is not smaller than -4. It's the other way around. I recommend looking at a number line to compare the two values.

This means that x-2 < x-4 is never true regardless of what x value you pick. So there are no solutions.