Question

is there any value of x with the property that x < x - 1? explain reasoning

Answer 1

$x\ \textless \ x-1\\ 0\ \textless \ -1$

The above is not true, so "no".

Answer 2

x < x-1
⇒ x -x < -1
⇒ 0 < -1 (false!)

Because that 0 < -1 is never true, there is no value of x with the property that x < x-1.

Hope this helps~