MATH SOLVE

3 months ago

Q:
# Which of the solution sets is all real numbers?IXI <-1IxI= -1lx|>-1

Accepted Solution

A:

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.