Brutus.
Need some Assistance. (x-3)^2/(x+1)(x-2)>0
I'm supposed to solve it and express my answer in interval notation.
Delete
Share
This Question is Closed
RaphaelFilgueiras
Best Response
You've already chosen the best response.
0
|dw:1372837027496:dw|
zzr0ck3r
Best Response
You've already chosen the best response.
1
is this \[\frac{(x-3)^{2}}{(x+1)(x-2)}\]?
Brutus.
Best Response
You've already chosen the best response.
0
Yes. that is the equation.
zzr0ck3r
Best Response
You've already chosen the best response.
1
ok so the top is >0 for all x does not equal 3 right?
Brutus.
Best Response
You've already chosen the best response.
0
Right.
zzr0ck3r
Best Response
You've already chosen the best response.
1
so we need to make sure the bottom is > 0 right?
Brutus.
Best Response
You've already chosen the best response.
0
Yes.
RaphaelFilgueiras
Best Response
You've already chosen the best response.
0
|dw:1372837247856:dw|
RaphaelFilgueiras
Best Response
You've already chosen the best response.
0
i have forgot 3
zzr0ck3r
Best Response
You've already chosen the best response.
1
the bottom is a parabola that opens up, what are its x intercepts?
Brutus.
Best Response
You've already chosen the best response.
0
-1,2 Right?
zzr0ck3r
Best Response
You've already chosen the best response.
1
right
zzr0ck3r
Best Response
You've already chosen the best response.
1
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?
Brutus.
Best Response
You've already chosen the best response.
0
So far yes.
zzr0ck3r
Best Response
You've already chosen the best response.
1
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
zzr0ck3r
Best Response
You've already chosen the best response.
1
(-infinity,-1)U(2,3)U(3,infinity)
Brutus.
Best Response
You've already chosen the best response.
0
Okay, I get it now.
zzr0ck3r
Best Response
You've already chosen the best response.
1
good deal:)
Brutus.
Best Response
You've already chosen the best response.
0
I have another quick question
zzr0ck3r
Best Response
You've already chosen the best response.
1
oki
Brutus.
Best Response
You've already chosen the best response.
0
I had another problem like this and I solved it and got x<-1. How would I write that in interval notation?
zzr0ck3r
Best Response
You've already chosen the best response.
1
(-infinity,-1)
zzr0ck3r
Best Response
You've already chosen the best response.
1
if it was <=
(-infinity,-1]
Brutus.
Best Response
You've already chosen the best response.
0
The original problem was
\[3(1-\frac{ 3 }{4 }x)>5-\frac{ 1 }{ 4 }x\]
zzr0ck3r
Best Response
You've already chosen the best response.
1
3-(9/4)x>5-(1/4)x
-(8/4)x>5-3
2x<-2
x<-1
correct
Brutus.
Best Response
You've already chosen the best response.
0
\[x <-1\] I wrote the interval notation like so (-infinity,-1). But for some reason, my professor marked off points and circled interval notation.
zzr0ck3r
Best Response
You've already chosen the best response.
1
you sure it didn't say set builder?
Brutus.
Best Response
You've already chosen the best response.
0
The question said Solve the inequalities and express your answer in Interval notation.
zzr0ck3r
Best Response
You've already chosen the best response.
1
just go talk to your teacher, I make mistakes grading all the time....
Brutus.
Best Response
You've already chosen the best response.
0
Okay, thank you!
zzr0ck3r
Best Response
You've already chosen the best response.
1
np
Brutus.
Best Response
You've already chosen the best response.
0
One more equation?
Brutus.
Best Response
You've already chosen the best response.
0
Inequality*
zzr0ck3r
Best Response
You've already chosen the best response.
1
sure
Brutus.
Best Response
You've already chosen the best response.
0
\[|\frac{x=1 }{ 4}|\ge4\]
zzr0ck3r
Best Response
You've already chosen the best response.
1
is that plus or minus?
Brutus.
Best Response
You've already chosen the best response.
0
I know your supposed to get two answers. I got one which was \[x \ge15\]
Brutus.
Best Response
You've already chosen the best response.
0
Plus. My bad
Brutus.
Best Response
You've already chosen the best response.
0
\[|\frac{ x+1 }{4 }|\]
zzr0ck3r
Best Response
You've already chosen the best response.
1
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
zzr0ck3r
Best Response
You've already chosen the best response.
1
the very last and should be or
zzr0ck3r
Best Response
You've already chosen the best response.
1
*when you have |a|>b we get a<b or a>-b
Brutus.
Best Response
You've already chosen the best response.
0
Okay, So if I want the other answer I set the 4 to a negative answer?
zzr0ck3r
Best Response
You've already chosen the best response.
1
so you have abs((x+1)/4)>=4
so
(x+1)/4>=4 gives the solutions you already have
zzr0ck3r
Best Response
You've already chosen the best response.
1
not exactly
zzr0ck3r
Best Response
You've already chosen the best response.
1
now we do
(x+1)/4<=-4
x+1<=-16
x<=-17
zzr0ck3r
Best Response
You've already chosen the best response.
1
set it negative and flip the sign
Brutus.
Best Response
You've already chosen the best response.
0
Ah, that's what confused me.. Didn't know what to do with my sign
zzr0ck3r
Best Response
You've already chosen the best response.
1
you could have done -(x+1)/4<=4
but as a rule I just make the "non absolute value side" negative
Brutus.
Best Response
You've already chosen the best response.
0
Good rule! With interval notation, how would I write this?
Brutus.
Best Response
You've already chosen the best response.
0
I think its
\[(-\infty,-17]U(\infty,15]\]
zzr0ck3r
Best Response
You've already chosen the best response.
1
(-infinity,-17]U[15,infinity)
zzr0ck3r
Best Response
You've already chosen the best response.
1
think of the number line, write it in the order it would fall on the number line
Brutus.
Best Response
You've already chosen the best response.
0
Oh, I see.
zzr0ck3r
Best Response
You've already chosen the best response.
1
and note that (infinity,5] does not make since, because if x were to be in there then
infinity < x < 5
zzr0ck3r
Best Response
You've already chosen the best response.
1
<=5
Brutus.
Best Response
You've already chosen the best response.
0
You lost me there..
Brutus.
Best Response
You've already chosen the best response.
0
But, Thank you so much for the help.