Question

Some help with absolute value inequalities?

Answer 1

@TheSmartOne @thomaster

Answer 2

|a| gives a positive/ zero number depending on a 's value
a positive number/zero can never be less than a negative number

Answer 3

What I'm confused about is that, how can the absolute value ever be less then a negative number? How do I answer this?

Answer 4

Interesting.. hmm

Answer 5

Honestly the choices make no sense to me either because I would use none of those ...
But if I had to guess what they want
|x|<a usually means you have an "and" statement to deal with
and if you select x<a and x>-a

Changing your problem just a bit so I don't completely do your problem for you:
so |3x-7|<-1 I guess we can say we will use 3x-7<-1 and 3x-7>1
and solving these inequalities we will see there is no intersection
No solution in other words to |3x-7|<-1
that is 3x-7<-1 gives 3x<6 which gives x<2
and 3x-7>1 gives 3x>8 and x>8/3


As the two graph shows these two little sets do not have an intersection.