which of the solution sets is all real numbers?
ixi < -1
ixi= -1
lx|> -1

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 .

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 is always ,

and on the other hand 0 is larger than -1 ()

Then using transitive property, we get:

which is still true for all real numbers.