I need help with Interval notation

- anonymous

I need help with Interval notation

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- schrodinger

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- anonymous

Okay , what kind of help ?

- theEric

Hi! Do you have some part of it in particular you need help with? Do you just want to understand it in general?

- anonymous

\[3/2 \ge x < \]

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## More answers

- anonymous

0 at the end

- theEric

So, you want to say that \(\frac{3}{2}\) is greater than or equal to \(x\), and \(x\) is less than \(0\)?
So, \(\frac{3}{2}\ge x\) and \(x\lt0\)?

- anonymous

Yes

- anonymous

wait

- anonymous

\[3/2 \ge x > 0\]

- theEric

I would try to visualize it on a number line quick. That usually helps.
Okay, I have to draw the picture quick.

- theEric

|dw:1378324975369:dw|

- amistre64

the hardest part tends to be in remembering which brackets to use

- theEric

Oh, here's a link!
http://www.mathsisfun.com/sets/intervals.html

- amistre64

think of the square bracket as an equal sign connected by a bar
|dw:1378325178389:dw|

- theEric

Now, in my picture, I drew the two inequalities. Where do they over lap? They overlap to the right of \(0\) up to where \(\frac{3}{2}\) is!

- theEric

Haha, nice @amistre64 !

- amistre64

\[a\le x

- amistre64

its the only way i know to keeo track of all these notations :)

- theEric

For that interval, \(\frac{3}{2}\ge x\gt0\), it starts just to the right of \(0\), so you want to NOT INCLUDE \(0\). You know? So you have to use a \((\).

- anonymous

So it's (3/2,0] ?

- theEric

And your interval include everything between \(0\) and \(\frac{3}{2}\), and \(\frac{3}{2}\). Since in includes \(\frac{3}{2}\), you want to use \(]\).

- theEric

@Juliaxo9 I think we always want the number on the left to be the lesser number, and the one on the right to be greater!

- theEric

You go from \(0\) to \(\frac{3}{2}\), then!

- anonymous

[0, 3/2) ?

- theEric

Close! So they're in the correct order!
\(\frac{3}{2}\ge x\gt0\)
Now look at the signs. \(x\gt0\), but not equal to \(0\). So, should you use \((\) to show "not equal," or \([\) to show "equal to."

- theEric

?*

- anonymous

Sorry I went to eat

- theEric

Haha, no problem!

- anonymous

(0, 3/2)

- theEric

Okay, so, I'll just read what that says, and you tell me if it is correct.
You are going from \(0\), but not including \(0\), to \(\frac{3}{2}\), but not including \(\frac{3}{2}\). So that's where \(x\) must be. Is that right?

- theEric

Based on \(\frac{3}{2}\ge x\gt0\)?

- anonymous

Yes

- theEric

It looks like \(\dfrac{3}{2}\) is greater than \(\sf or\ equal\ to\) \(x\), right?

- theEric

\(\ge\)

- theEric

\(\dfrac{3}{2}\ge x\)
means
\(\dfrac{3}{2} > x\) or \(\dfrac{3}{2}=x\)
So, \(x\) can be \(\dfrac{3}{2}\), so you want to say that with a \(]\)!
:)

- theEric

So,
\(\left(0,~\dfrac{3}{2}\right]\)

- anonymous

but I thought 3/2 is bigger so it's first

- theEric

I think, with that interval notation, you want the smaller number on the left.
\(\left( lesser,\ greater\right]\)

- theEric

like \((-51,\ 10]\)

- theEric

I have to go, but feel free to check out the link I posted! Take care!

- anonymous

Ohh! Ok!

- anonymous

Can you check few for me?

- anonymous

\[-4 < x < \]

- anonymous

4 at the end sorry

- anonymous

(-4,4) ?

- anonymous

@theEric

- anonymous

nvm got it thank you!!!

- theEric

You are correct! :)

- anonymous

:)

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