## anonymous 5 years ago need to solve inequality in interval notation and algebraic notation.

1. anonymous

$x+2 \over x+6$>0

2. anonymous

the x+2 is a fraction over x+6 and it's supposed to be in a straight line with >0

3. anonymous

okay flip it. so we get (x+6)/(x+2)>0 x+6 = x+2 +4 1+4/(x+2)>0 4/(x+2) > -1 4>(-x-2) 4<(x+2)

4. anonymous

sorry the last step is -4 < x+2

5. anonymous

got it?

6. anonymous

oh ok. yeah, makes sense. so which one is the interval notation and which ones the algebraic. Just to clarify?

7. anonymous

it says to separate answers in algebraic notation with or if necessary. I wasn't sure if there was more than one.

8. anonymous

oh I didnt see that part of the problem. x > -6 is the algebraic notation x = {-5 to +infinity} (or something like that) would be interval notation. the two are different methods of expressing all the values x can take. you can either say x is greater than negative 6 ( x>-6) or you can say x can take any value between -5 and positive infinity x = {-5 to +infinity} I don't remember how the interval notation works. google it.

9. anonymous

ok so the only think I should put down for algebraic notation is $x >-6$? I don't think it wants me to say the same thing twice, It might want me to put or in between if their is another solution?

10. anonymous

there is no 'other' solution. x lies in a certain interval. How you say that x lies in a certain interval changes. You can either say x> 6 but x<9 or you can say x lies between 6 and 9.

11. anonymous

The problem states you need to express it in both notations.

12. anonymous

ohh I see what you were saying. ok. Thanks

13. anonymous

lol, you are welcome.

14. anonymous

think $-5,\infty$ is the answer to the other part of the problem? or should I double check somewhere?

15. anonymous

for the interval notation.

16. anonymous

would this be either of the answers? http://www.wolframalpha.com/input/?i=%28x%2B2%29%2F%28x%2B6%29%3E0

17. anonymous

Yes, that is right. the first solution is the algebraic notation. the second solution is the interval notation, only it is expressed in graphical form.