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hi, can someone help me write this in set notation, find the solution and write it in interval notation, and how to graph it
First, subtract 1 from both sides
what should I do next
Use the draw feature to Post your work
sorry it's really messy
That's perfect. Next rewrite 1 As A fraction So that both fractions have the same denominator
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?
Awesome . Now you can combine the fractions but be careful. am going to help you with this next step.
Hang on a minute.
the denominator doesn't cancel out?
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
i did and i got 1 :/
Let me ask you this: What is 5/6 minus 2/6
How come you didn't do 6-6 to get zero?
ok so now it's|dw:1442686906249:dw|
that's how i learned it you don't subtract when they're the same :) ok i see what you're saying
perfect. Now factor the denominator.
Very good. Now we should make A number line and plot our critical points. Any ideas on that?
what're critical points?
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
3 and -2?
correct, now draw a number line that induces those points.
Or rather, that excludes those points. Hence open circle
is that correct
The reason you want to Write it that way is because it shows three distinct intervals that we can work with.
One easy convenient Value We can test is x=0
If it passes the test, then the interval x=0 comes from is at least one Of the solutions
it does not pass it
Okay, if not then, We can eliminate that interval ( -2 , 3) as a possible solution
try testing one value from each of the other two Intervals.
-1 does not work either
-1 is from the interval ( -2 , 3)
We already eliminated that Interval
wait but 1 worked
Okay sorry, We need to line modify our number line because 1 is also a critical point.
okay i see
the circle is shaded in for 1 right?
ok nice nice
So We have 4 intervals now that We need to test. Pick values from each.
2 is true
Let me know what works and What doesn't
-3 also works
I agree the 2 And-3 Works. Anything else?
-3 and -4 are from the sand Interval. pµc values from the Other two intervals you haven't checked yet
same interval *
4 does not work
I've tried from all intervals now
-1 and 0 don't
and 4 does not
So what is the solution for the original inequality?
in interval notation it'd be
Congratulations, you've earned a medal for your hard work.
thank you!! can you tell me the difference between set notation and interval notation?
Here's a good tutorial that explains well enough:http://www.regentsprep.org/regents/math/algebra/ap1/intervalnot.htm
If you have any questions about it feel free to ask
i understand the interval notation but the set notation throws me off, how could i write it
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
what're descriptive components
okay so in this case i want to represent the number line right
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
Yes, give it a Shot
Well, not exactly. First you hare to rewrite each Interval notation as an inequality.
how could i do that
For example ( a,b) means the same as a
Okay, now Write the set notation and include all the appropriate Components,
Oh, don't forget to use the correct inequality symbol for Inclusion
That's almost perfect but we don't know what Kind of set x IS.
mm what do you mean?
X belongs to what kind of Set? Integers?, natural numbers? Real Numbers?
Add that to your set builder notation.
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
Create a new question though.