4w + 6 -2 and 2w - 4 4

I have it all done, but what would be the interval notation if the "and" statement is going all toward the infinity direction?

Question

4w + 6 > -2 and  2w - 4 > 4

I have it all done, but what would be the interval notation if the "and" statement is going all toward the infinity direction?

anonymous · Answer

Let's use x > 6 as an example.  Then for the interval notation you would have:$$(6, \infty)$$Notice how the infinity has a ")" instead of "]".  That is because you cannot "bound" infinity.  It's just a notation convention that has to be committed to memory, but the above explanation has always helped me a bit.

artfis · Answer

Ok right I do understand that, but I have trouble depicting on the number line when the solution becomes 
w > -2 AND w > 4. ??

anonymous · Answer

np.  You are actually almost done.  The word "and" means that you are looking for the intersection or the "overlap".  I'll try to draw a picture.  Hold on...

artfis · Answer

I found the overlap to be past the w > 4....

anonymous · Answer

|dw:1359842295487:dw|

anonymous · Answer

Yes!  Good work!  the bottom one is -2 < w, the middle is 4 < w and the top is the overlap, but I think you got it now.

artfis · Answer

So the interval notation should be (-2, infinity) U (4, infinity) :D right?

anonymous · Answer

Not union, intersection.  And it is just 4 < w because every point in 4 < w is in -2 < w.  Remember, you want the overlap, and in my drawing, the top and middle lines are the same, so the overlap or intersection is just 4 < w.  It's tricky at first, but if you mull it over, it will stick in the old noggin.

anonymous · Answer

$$(4, \infty)$$So, the same as (4, infinity)

artfis · Answer

OH OK! It makes more sense for me. You helped me a lot with this . Thank you so much. :)

anonymous · Answer

You're quite welcome!  Good luck to you in all of your studies and thx for the recognition! @ArTFis