heyitslizzy13
  • heyitslizzy13
can someone help me please!(:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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heyitslizzy13
  • heyitslizzy13
hi, can someone help me write this in set notation, find the solution and write it in interval notation, and how to graph it
Hero
  • Hero
First, subtract 1 from both sides

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heyitslizzy13
  • heyitslizzy13
ok :)
heyitslizzy13
  • heyitslizzy13
what should I do next
Hero
  • Hero
Use the draw feature to Post your work
heyitslizzy13
  • heyitslizzy13
|dw:1442685887228:dw|
heyitslizzy13
  • heyitslizzy13
sorry it's really messy
Hero
  • Hero
That's perfect. Next rewrite 1 As A fraction So that both fractions have the same denominator
heyitslizzy13
  • heyitslizzy13
|dw:1442686057579:dw|
Hero
  • Hero
That's a good start I suppose. But we need both fractions to have the same denominator. Remember, anything over itself Is 1 . Can you think of a way to rewrite 1 so that both fractions have the same denominator?
heyitslizzy13
  • heyitslizzy13
|dw:1442686299242:dw|
Hero
  • Hero
Awesome . Now you can combine the fractions but be careful. am going to help you with this next step.
heyitslizzy13
  • heyitslizzy13
ok
Hero
  • Hero
Hang on a minute.
heyitslizzy13
  • heyitslizzy13
alrighty :)
Hero
  • Hero
heyitslizzy13
  • heyitslizzy13
the denominator doesn't cancel out?
Hero
  • Hero
when you rewrite 1 as a fraction, especially When doing subtraction of algebraic expressions, you should make a habit of placing parenthesis around the egression in the numerator so that you remember to distribute the negative
heyitslizzy13
  • heyitslizzy13
i did and i got 1 :/
Hero
  • Hero
Let me ask you this: What is 5/6 minus 2/6
heyitslizzy13
  • heyitslizzy13
|dw:1442686808756:dw|
heyitslizzy13
  • heyitslizzy13
3/6
heyitslizzy13
  • heyitslizzy13
i seeee
Hero
  • Hero
How come you didn't do 6-6 to get zero?
heyitslizzy13
  • heyitslizzy13
ok so now it's|dw:1442686906249:dw|
heyitslizzy13
  • heyitslizzy13
that's how i learned it you don't subtract when they're the same :) ok i see what you're saying
Hero
  • Hero
perfect. Now factor the denominator.
heyitslizzy13
  • heyitslizzy13
|dw:1442686993828:dw|
Hero
  • Hero
Very good. Now we should make A number line and plot our critical points. Any ideas on that?
heyitslizzy13
  • heyitslizzy13
what're critical points?
Hero
  • Hero
The critical points are the values On the number line that are not in the domain of the expression' They are the values that x Cannot equal
heyitslizzy13
  • heyitslizzy13
3 and -2?
Hero
  • Hero
correct, now draw a number line that induces those points.
heyitslizzy13
  • heyitslizzy13
|dw:1442687325243:dw|
Hero
  • Hero
Or rather, that excludes those points. Hence open circle
heyitslizzy13
  • heyitslizzy13
is that correct
Hero
  • Hero
I recommend writing the number line this way for clarity And Simplicity
heyitslizzy13
  • heyitslizzy13
okay
Hero
  • Hero
The reason you want to Write it that way is because it shows three distinct intervals that we can work with.
heyitslizzy13
  • heyitslizzy13
alright
Hero
  • Hero
Next we Will test convenient Values between the critical points by inserting those convenient points from each interval into the factored expression.
Hero
  • Hero
One easy convenient Value We can test is x=0
Hero
  • Hero
If it passes the test, then the interval x=0 comes from is at least one Of the solutions
heyitslizzy13
  • heyitslizzy13
it does not pass it
Hero
  • Hero
Okay, if not then, We can eliminate that interval ( -2 , 3) as a possible solution
Hero
  • Hero
try testing one value from each of the other two Intervals.
heyitslizzy13
  • heyitslizzy13
-1 does not work either
heyitslizzy13
  • heyitslizzy13
1 works
Hero
  • Hero
-1 is from the interval ( -2 , 3)
Hero
  • Hero
We already eliminated that Interval
heyitslizzy13
  • heyitslizzy13
wait but 1 worked
Hero
  • Hero
Okay sorry, We need to line modify our number line because 1 is also a critical point.
heyitslizzy13
  • heyitslizzy13
oh yeahhhhh
heyitslizzy13
  • heyitslizzy13
okay i see
heyitslizzy13
  • heyitslizzy13
the circle is shaded in for 1 right?
Hero
  • Hero
heyitslizzy13
  • heyitslizzy13
ok nice nice
Hero
  • Hero
So We have 4 intervals now that We need to test. Pick values from each.
heyitslizzy13
  • heyitslizzy13
2 is true
Hero
  • Hero
Let me know what works and What doesn't
heyitslizzy13
  • heyitslizzy13
-3 also works
Hero
  • Hero
I agree the 2 And-3 Works. Anything else?
heyitslizzy13
  • heyitslizzy13
-4 also
Hero
  • Hero
-3 and -4 are from the sand Interval. pµc values from the Other two intervals you haven't checked yet
Hero
  • Hero
same interval *
heyitslizzy13
  • heyitslizzy13
4 does not work
heyitslizzy13
  • heyitslizzy13
I've tried from all intervals now
heyitslizzy13
  • heyitslizzy13
-3 works
heyitslizzy13
  • heyitslizzy13
-1 and 0 don't
heyitslizzy13
  • heyitslizzy13
2 works
heyitslizzy13
  • heyitslizzy13
and 4 does not
Hero
  • Hero
So what is the solution for the original inequality?
heyitslizzy13
  • heyitslizzy13
in interval notation it'd be
heyitslizzy13
  • heyitslizzy13
|dw:1442689021631:dw|
Hero
  • Hero
Congratulations, you've earned a medal for your hard work.
heyitslizzy13
  • heyitslizzy13
thank you!! can you tell me the difference between set notation and interval notation?
Hero
  • Hero
Here's a good tutorial that explains well enough:http://www.regentsprep.org/regents/math/algebra/ap1/intervalnot.htm
Hero
  • Hero
If you have any questions about it feel free to ask
heyitslizzy13
  • heyitslizzy13
i understand the interval notation but the set notation throws me off, how could i write it
Hero
  • Hero
i. We use curly brackets for set notation. ii The vertical bar separates two descriptive Components The Componentt to the left of the bar identifies the variable and the number line used. In this case, the variable is x And the number line represents all real numbers. The component to the right't the vertical bar simply identities ' the Solution interval
heyitslizzy13
  • heyitslizzy13
what're descriptive components
heyitslizzy13
  • heyitslizzy13
okay so in this case i want to represent the number line right
Hero
  • Hero
The descriptive components of a set are simply mathematical statements or expressions used to identify things like the variable, the number line and the interval Of interest. These things just simply tell you how to re-construct the number line
Hero
  • Hero
Yes, give it a Shot
heyitslizzy13
  • heyitslizzy13
|dw:1442690853126:dw| ://
Hero
  • Hero
Well, not exactly. First you hare to rewrite each Interval notation as an inequality.
heyitslizzy13
  • heyitslizzy13
how could i do that
Hero
  • Hero
For example ( a,b) means the same as a
heyitslizzy13
  • heyitslizzy13
|dw:1442691229604:dw|
Hero
  • Hero
Okay, now Write the set notation and include all the appropriate Components,
Hero
  • Hero
Oh, don't forget to use the correct inequality symbol for Inclusion
heyitslizzy13
  • heyitslizzy13
|dw:1442691352299:dw|
Hero
  • Hero
That's almost perfect but we don't know what Kind of set x IS.
heyitslizzy13
  • heyitslizzy13
mm what do you mean?
Hero
  • Hero
X belongs to what kind of Set? Integers?, natural numbers? Real Numbers?
heyitslizzy13
  • heyitslizzy13
real numbers
Hero
  • Hero
Correct
Hero
  • Hero
Add that to your set builder notation.
heyitslizzy13
  • heyitslizzy13
thank you!!(: can you help me on one more problem? I've started it but i'm not sure if i'm doing it correctly
Hero
  • Hero
Okay
Hero
  • Hero
Create a new question though.
heyitslizzy13
  • heyitslizzy13
okay

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