## Brutus. Group Title Need some Assistance. (x-3)^2/(x+1)(x-2)>0 I'm supposed to solve it and express my answer in interval notation. one year ago one year ago

1. RaphaelFilgueiras Group Title

|dw:1372837027496:dw|

2. zzr0ck3r Group Title

is this $\frac{(x-3)^{2}}{(x+1)(x-2)}$?

3. Brutus. Group Title

Yes. that is the equation.

4. zzr0ck3r Group Title

ok so the top is >0 for all x does not equal 3 right?

5. Brutus. Group Title

Right.

6. zzr0ck3r Group Title

so we need to make sure the bottom is > 0 right?

7. Brutus. Group Title

Yes.

8. RaphaelFilgueiras Group Title

|dw:1372837247856:dw|

9. RaphaelFilgueiras Group Title

i have forgot 3

10. zzr0ck3r Group Title

the bottom is a parabola that opens up, what are its x intercepts?

11. Brutus. Group Title

-1,2 Right?

12. zzr0ck3r Group Title

right

13. zzr0ck3r Group Title

so the bottom is greater than 0 when x<-1 and x>2, because it opens up and crosses y=0 at -1,2 with me?

14. Brutus. Group Title

So far yes.

15. zzr0ck3r Group Title

so we know the top is grater than 0 when x is not 3 we know the bottom is greater than 0 when x<-1 and x>2 so the whole thing is greater than 0 when x<-1 and x>2 and x does not equal 3

16. zzr0ck3r Group Title

(-infinity,-1)U(2,3)U(3,infinity)

17. Brutus. Group Title

Okay, I get it now.

18. zzr0ck3r Group Title

good deal:)

19. Brutus. Group Title

I have another quick question

20. zzr0ck3r Group Title

oki

21. Brutus. Group Title

I had another problem like this and I solved it and got x<-1. How would I write that in interval notation?

22. zzr0ck3r Group Title

(-infinity,-1)

23. zzr0ck3r Group Title

if it was <= (-infinity,-1]

24. Brutus. Group Title

The original problem was $3(1-\frac{ 3 }{4 }x)>5-\frac{ 1 }{ 4 }x$

25. zzr0ck3r Group Title

3-(9/4)x>5-(1/4)x -(8/4)x>5-3 2x<-2 x<-1 correct

26. Brutus. Group Title

$x <-1$ I wrote the interval notation like so (-infinity,-1). But for some reason, my professor marked off points and circled interval notation.

27. zzr0ck3r Group Title

you sure it didn't say set builder?

28. Brutus. Group Title

The question said Solve the inequalities and express your answer in Interval notation.

29. zzr0ck3r Group Title

he/she is wrong http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm look at non ending interval note: we have ) not ] because we have < not <=

30. zzr0ck3r Group Title

just go talk to your teacher, I make mistakes grading all the time....

31. Brutus. Group Title

Okay, thank you!

32. zzr0ck3r Group Title

np

33. Brutus. Group Title

One more equation?

34. Brutus. Group Title

Inequality*

35. zzr0ck3r Group Title

sure

36. Brutus. Group Title

$|\frac{x=1 }{ 4}|\ge4$

37. zzr0ck3r Group Title

is that plus or minus?

38. Brutus. Group Title

I know your supposed to get two answers. I got one which was $x \ge15$

39. Brutus. Group Title

40. Brutus. Group Title

$|\frac{ x+1 }{4 }|$

41. zzr0ck3r Group Title

ok so this is strange and you may need to think about it a bit, but when you have |a|=b we get a=b and a=-b when you have |a|<b we get -b<x<b when you have |a|>b we get a<b and a>-b

42. zzr0ck3r Group Title

the very last and should be or

43. zzr0ck3r Group Title

*when you have |a|>b we get a<b or a>-b

44. Brutus. Group Title

Okay, So if I want the other answer I set the 4 to a negative answer?

45. zzr0ck3r Group Title

so you have abs((x+1)/4)>=4 so (x+1)/4>=4 gives the solutions you already have

46. zzr0ck3r Group Title

not exactly

47. zzr0ck3r Group Title

now we do (x+1)/4<=-4 x+1<=-16 x<=-17

48. zzr0ck3r Group Title

set it negative and flip the sign

49. Brutus. Group Title

Ah, that's what confused me.. Didn't know what to do with my sign

50. zzr0ck3r Group Title

you could have done -(x+1)/4<=4 but as a rule I just make the "non absolute value side" negative

51. Brutus. Group Title

Good rule! With interval notation, how would I write this?

52. Brutus. Group Title

I think its $(-\infty,-17]U(\infty,15]$

53. zzr0ck3r Group Title

(-infinity,-17]U[15,infinity)

54. zzr0ck3r Group Title

think of the number line, write it in the order it would fall on the number line

55. Brutus. Group Title

Oh, I see.

56. zzr0ck3r Group Title

and note that (infinity,5] does not make since, because if x were to be in there then infinity < x < 5

57. zzr0ck3r Group Title

<=5

58. Brutus. Group Title

You lost me there..

59. Brutus. Group Title

But, Thank you so much for the help.