## anonymous 5 years ago For the inequality x+2 over x+6>0. Need clarification on interval notation and algebraic notation solution

1. anonymous

for algebraic notation I have x>-2 or x<-6. Anyone know if this is correct and what the interval notation looks like?

2. anonymous

This is my last problem on my online assignment and I can't get any more wrong or i have to start over so i'm trying to make sure I get the right format. In case you're wondering why I have this up here again. ha

3. anonymous

There is this thing called google. I used it to find this particular website. You might wanna check it out. http://zonalandeducation.com/mmts/miscellaneousMath/intervalNotation/intervalNotation.html

4. anonymous

yeah, I looked at that too. I just don't see how this looks different than the algebraic answer.

5. anonymous

um, algebraic notation is x>-2 or x<-6 the interval notation is x = { (- infinity, -6) , (-2, infinity)}

6. anonymous

how do the two look same to you?

7. anonymous

do they have to have the {} around them? So for x+1/x+7>0 here I got alg: x>-1 or x<-7. will the notation one be $\left\{ -\infty,-7 \right\}\left\{ -1,\infty \right\}$

8. anonymous

I just posted a link as to how interval notation works. Read it.

9. anonymous

It is better than reading my explanation.

10. anonymous

x = (5,7) means that x lies between, BUT NOT including 5 and 7. x = [5,7] means that x lies between AND including 5 and 7 x = [5,7) means that x lies between 5 and 7, including 5, but not 7.

11. anonymous

Yeah I was looking at that. Just wasn't positive on which one to put for this problem. Wasn't even sure if I have the right solution to go off of

12. anonymous

okay let me ask you a question what does x>5 mean to you?

13. anonymous

x=-5?

14. anonymous

wait. nvm

15. anonymous

what? NO! how does that even make any sense? Just tell me in plain english what you mean by x > 5.

16. anonymous

x is greater than 5.. I didn't realize how simple the question was. I misread what you wrote first.

17. anonymous

yes. So x is greater than 5. does that mean that the value of x lies between 5 and infinity?

18. anonymous

yes

19. anonymous

okay, but does it also mean that x could be 5?

20. anonymous

no because it isn't greater or equal to

21. anonymous

okay good. so x lies between 5 and infinity, including infinity, BUT NOT including 5. so we write x = (5, infinity]

22. anonymous

just remember, parentheses ( ) mean not including. square brackets [ ] mean including

23. anonymous

$[-\infty,-7)(-1,\infty]$ Sorry for being so annoying I just want to make sure this one looks correct before I submit it. Think this is the answer to the x+1/x+7>0?

24. anonymous

Also, thanks for explaining that. It makes sense now. Just want to get the correct format

25. anonymous

yes, that is right. that should be the answer to the second one. you are welcome. it is better to understand what you are talking about rather than just follow what others say.

26. anonymous

it wont et me only put the [ on one side. maybe it needs to be in this format.. [-inf(-7-1)int]

27. anonymous

no, that is incorrect format. you dont need to put square brackets for infinity, because infinity can never really be reached. so it doesn't matter.

28. anonymous

you should have read the article I posted. that link explains what you need to do. Well, let us get just a bit more complicated. Using interval notation we will show the set of number that includes all real numbers except 5. First, stated as inequalities this group looks like this: The statement using the inequalities above joined by the word or means that x is a number in the set we just described, and that you will find that number somewhere less than 5 or somewhere greater than 5 on the number line. In interval notation a logically equivalent statement does not use the word or, but rather a symbol for what is called the union of two groups of numbers. The symbol for union coincidentally looks like a U, the first letter of union. However, it is really not a letter of the alphabet. Here is what the union symbol looks like: U So, the group of numbers that includes all values less than 5 and all values greater than 5, but does not include 5 itself, expressed as interval notation looks like this: $(-\infty,5) \cup (5,+\infty)$