What the absolute value of three times a number, n, is greater than 15?

Here is a number line representation.          $$|3n|>15$$

All the little end circles are meant to be open, that is because there is no equal sign so the end points are NOT included.

ity_o28q/12s40x.jpg             ヽ(ヅ)ノ

Absolute value of 3n>15

Absolute value of n>5

n>5 or n<-5 Since the absolute value turns the negative into a positive and <-5 would be more than 5 when you remove the negative symbol. This is easily shown on a number line but I don't know how to draw one.

May I ask how you drew/made one?

Nice diagram Melody!I havent seen such a neat numberline!Thumbs up from me!

Of course you may Quazars.

I used GeoGebra.  It is a free download. 

Just muck around with it and you will slowly get the idea.  It is not very intuitive I am afraid but it is not impossible either.

I do not know how to use it very well.  It is quite powerful.  I'm slowly getting better with it.

I only worked out how to do number lines a short time ago.

download it and start playing - That is my advice.  It is fun.

Oh - And thank you Rosala 

Your Welcome Melody!

That was a nice graphical answer by Melody......let's see how we might arrive at the answer using a little Algebra.

Note one thing........   l 7 l = 7   and  l -7 l = 7

This must imply that  we can find some positive values of 3n that are greater than 15 and that we also can find some negative values of 3n that are greater than 15.

Therefore, we have

3n > 15     so  n > 5

And

-3n > 15   so   n < -5 

So our solution set would be (-∞, -5) U (5, ∞)

As Melody has shown.......!!!!