Question

Solve the absolute value inequality: |x - 4| > 2

x < 2 or x > 6

x > 2 or x < 6

x < -6 or x > 6

x > 2 and x < 6



I got x > 6 or < -2
But as you can see, that is not a choice, please help, thank you.

Answer 1

If |f(x)|>2, this means f(x)>2 or f(x)<-2.
If |f(x)|<2, this means -2<f(x)<2

Answer 2

I'm saying f(x)=x-4
Just replace my f(x) above with x-4.

Answer 3

Well think of the absolute value as parentheses for now and get x by itself so you would get absolute value of x > 6. So it would actually be answer C.

Answer 4

No...

Answer 5

Pretend if we just had |x|>2
This means what values of x have a distance from 0 greater than 2.
Draw a number line if you think it helps.

<---|-----|-------|------|-----|--->
-4 -2 0 2 4

What number have a distance greater than 2 from 0?
All the values less than -2 or greater than 2 will give you numbers that have a distance greater than 2 from 0.

So that means if we had |x|>2
then x<-2 or x>2 based on what we just said in words.

So if we have |f(x)|>2
this means we have f(x)<-2 or f(x)>2

Answer 6

Can you break that down in a more simple way, because replacing X with F and stuff is really confusing me.

Answer 7

Replace f(x) with x-4
not x with f

|f(x)|>2 means f(x)>2 or f(x)<-2
|x-4|>2 means x-4>2 or x-4<-2

Answer 8

Where does the f come to play in this?

Answer 9

And I keep on getting the same answer :(

Answer 10

f(x) is x-4

I put what |x-4|>2 means
It means x-4>2 or x-4<-2

I think you aren't solving the second inequality right.
You are adding 4 on both sides right?
x-4>2 or x-4<-2
x-4+4>4+2 or x-4+4<-2+4