need to solve inequality in interval notation and algebraic notation.

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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)

anonymous · Answer

sorry the last step is -4 < x+2

anonymous · Answer

got it?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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?

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

ohh I see what you were saying. ok. Thanks

anonymous · Answer

lol, you are welcome.

anonymous · Answer

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

anonymous · Answer

for the interval notation.

anonymous · Answer

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

anonymous · Answer

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.