Question

What is the solution of |x – 2| > –3? Explain.

Answer 1

x> -1 can be one

Answer 2

when doing absolute value inequalities you always want to set one positive and one negative.

|x – 2| > –3 and |x – 2| > 3

Answer 3

So Do I Solve For Both Equations?

Answer 4

Yes

Answer 5

@genny7 will |x-2|'s output always be positive or 0?

Answer 6

I really dont know?

Answer 7

for all x you think about plugging in

Answer 8

like think about | | means distance
isn't distance always positive or zero?

Answer 9

positive?

Answer 10

that is a yes or no question

Answer 11

yes

Answer 12

so |x-2| wouldn't that always be greater than a negative number?

Answer 13

yes it would be greater

Answer 14

ok so what is your answer to |x-2|>-3 ?

Answer 15

she should get x > 1 and x >5 as her answers

Answer 16

no @Glorenda49

Answer 17

|x-2| for any real value x is positive or zero
|x-2| will always be greater than any negative number for any real value x

Answer 18

That's not how I learned it

Answer 19

Example of your answer being false
your answer doesn't include 0
if x=0 then |0-2|=|-2|=2
isn't 2>-3?

your answer doesn't include -1000
if x=-1000 then |-1000-2|=|-1002|=1002
isn't 1002>-3?

Answer 20

those are just two examples
I could provide infinitely more examples of your answer not including all solutions

Answer 21

So the solution would not be 1 or 5?

Answer 22

I already said the solution way above
The solution does include 1 or 5
It also includes all other real numbers

Answer 23

No i see my mistake.. i'm sorry genny

Answer 24

Oh okay I understand now!

Answer 25

Its okay Glorenda :)

Answer 26

now if we had had |x-2|>3
then you would do x-2>3 or x-2<-3
and solve both inequalities to get your whole answer


but whenever you have |x|>negative number
the solution is all real numbers (or you can even say all complex numbers)

Answer 27

what would the solution be to this:
solve |x|<-5 ?

Answer 28

think
can |x| ever be negative?
is |x| positive or zero for any real number x?

Answer 29

positive

Answer 30

|x| is positive or zero for any real value x
which means it is always greater than any negative number
but |x|<-5 contradicts that
therefore |x|<-5 has no solution

Answer 31

there is no number you can plug in for x such that |x|<-5

Answer 32

ok

Answer 33

anyways i hope you understand better what absolute value means
and that it can only be either positive or zero output for it

Answer 34

Yes i do understand it a little better! :) And Thanks SOOOOOOO Much For Your Help!