Answer:
[tex]|x|>-1[/tex]
Step-by-step explanation:
Recall that the function absolute value of any real number gives always a non-negative answer. That is |x| is always [tex]\geq 0[/tex].
Therefore,
1) the first statement will be the empty/Null set (there are no real numbers whose absolute value can be smaller that negative one.
2) Something similar happens with the second statement: the absolute value of a real number cannot be equal to a negative number (in this case "-1". So this set is the empty/Null set.
3) Since we know from our statement above that [tex]|x|[/tex] is always [tex]\geq 0[/tex],
and on the other hand 0 is larger than -1 ([tex]0>-1[/tex])
Then using transitive property, we get:
[tex]|x|\geq 0>-1\\|x|>-1[/tex] which is still true for all real numbers.
