can someone help me please!(:

- heyitslizzy13

can someone help me please!(:

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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

First, subtract 1 from both sides

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## More answers

- heyitslizzy13

ok :)

- heyitslizzy13

what should I do next

- Hero

Use the draw feature to Post your work

- heyitslizzy13

|dw:1442685887228:dw|

- heyitslizzy13

sorry it's really messy

- Hero

That's perfect. Next rewrite 1 As A fraction So that both fractions have the same denominator

- heyitslizzy13

|dw:1442686057579:dw|

- 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

|dw:1442686299242:dw|

- Hero

Awesome . Now you can combine the fractions but be careful. am going to help you with this next step.

- heyitslizzy13

ok

- Hero

Hang on a minute.

- heyitslizzy13

alrighty :)

- Hero

##### 1 Attachment

- heyitslizzy13

the denominator doesn't cancel out?

- 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

i did and i got 1 :/

- Hero

Let me ask you this: What is 5/6 minus 2/6

- heyitslizzy13

|dw:1442686808756:dw|

- heyitslizzy13

3/6

- heyitslizzy13

i seeee

- Hero

How come you didn't do 6-6 to get zero?

- heyitslizzy13

ok so now it's|dw:1442686906249:dw|

- heyitslizzy13

that's how i learned it you don't subtract when they're the same :) ok i see what you're saying

- Hero

perfect. Now factor the denominator.

- heyitslizzy13

|dw:1442686993828:dw|

- Hero

Very good. Now we should make A number line and plot our critical points. Any ideas on that?

- heyitslizzy13

what're critical points?

- 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

3 and -2?

- Hero

correct, now draw a number line that induces those points.

- heyitslizzy13

|dw:1442687325243:dw|

- Hero

Or rather, that excludes those points. Hence open circle

- heyitslizzy13

is that correct

- Hero

I recommend writing the number line this way for clarity And Simplicity

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- heyitslizzy13

okay

- Hero

The reason you want to Write it that way is because it shows three distinct intervals that we can work with.

- heyitslizzy13

alright

- Hero

Next we Will test convenient Values between the critical points by inserting those convenient points from each interval into the factored expression.

##### 1 Attachment

- Hero

One easy convenient Value We can test is x=0

- Hero

If it passes the test, then the interval x=0 comes from is at least one Of the solutions

- heyitslizzy13

it does not pass it

- Hero

Okay, if not then, We can eliminate that interval ( -2 , 3) as a possible solution

- Hero

try testing one value from each of the other two Intervals.

- heyitslizzy13

-1 does not work either

- heyitslizzy13

1 works

- Hero

-1 is from the interval ( -2 , 3)

- Hero

We already eliminated that Interval

- heyitslizzy13

wait but 1 worked

- Hero

Okay sorry, We need to line modify our number line because 1 is also a critical point.

- heyitslizzy13

oh yeahhhhh

- heyitslizzy13

okay i see

- heyitslizzy13

the circle is shaded in for 1 right?

- Hero

##### 1 Attachment

- heyitslizzy13

ok nice nice

- Hero

So We have 4 intervals now that We need to test. Pick values from each.

- heyitslizzy13

2 is true

- Hero

Let me know what works and What doesn't

- heyitslizzy13

-3 also works

- Hero

I agree the 2 And-3 Works. Anything else?

- heyitslizzy13

-4 also

- Hero

-3 and -4 are from the sand Interval. pÂµc values from the Other two intervals you haven't checked yet

- Hero

same interval *

- heyitslizzy13

4 does not work

- heyitslizzy13

I've tried from all intervals now

- heyitslizzy13

-3 works

- heyitslizzy13

-1 and 0 don't

- heyitslizzy13

2 works

- heyitslizzy13

and 4 does not

- Hero

So what is the solution for the original inequality?

- heyitslizzy13

in interval notation it'd be

- heyitslizzy13

|dw:1442689021631:dw|

- Hero

Congratulations, you've earned a medal for your hard work.

- heyitslizzy13

thank you!! can you tell me the difference between set notation and interval notation?

- Hero

Here's a good tutorial that explains well enough:http://www.regentsprep.org/regents/math/algebra/ap1/intervalnot.htm

- Hero

If you have any questions about it feel free to ask

- heyitslizzy13

i understand the interval notation but the set notation throws me off, how could i write it

- 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

what're descriptive components

- heyitslizzy13

okay so in this case i want to represent the number line right

- 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

Yes, give it a Shot

- heyitslizzy13

|dw:1442690853126:dw| ://

- Hero

Well, not exactly. First you hare to rewrite each Interval notation as an inequality.

- heyitslizzy13

how could i do that

- Hero

For example ( a,b) means the same as a

- heyitslizzy13

|dw:1442691229604:dw|

- Hero

Okay, now Write the set notation and include all the appropriate Components,

- Hero

Oh, don't forget to use the correct inequality symbol for Inclusion

- heyitslizzy13

|dw:1442691352299:dw|

- Hero

That's almost perfect but we don't know what Kind of set x IS.

- heyitslizzy13

mm what do you mean?

- Hero

X belongs to what kind of Set? Integers?, natural numbers? Real Numbers?

- heyitslizzy13

real numbers

- Hero

Correct

- Hero

Add that to your set builder notation.

- 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

Okay

- Hero

Create a new question though.

- heyitslizzy13

okay

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