write the solution in interval notation using the union sign U
2y+5<5y-1 or 5y-1<3y-7

- shreenithaa

write the solution in interval notation using the union sign U
2y+5<5y-1 or 5y-1<3y-7

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- shreenithaa

@ganeshie8
@zepdrix

- zepdrix

\[\large\rm 2y+5\lt 5y-1\]What do you get when you simplify? :)

- shreenithaa

2y+5<5y-1 or 5y-1<3y-7
-5 -5 +1 +1
2y<5y-6 or 5y<3y-6
-5y -5y -3y -3y
-3y<6 or 2y<-8
////////////////
-3 2
y>-2 or y<-4

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## More answers

- shreenithaa

@zepdrix

- shreenithaa

how do u write the interval notation using the union sign

- zepdrix

Hmm, those don't look quite right.
Here is what I would recomment for the first relationship.\[\large\rm 2y+5\lt 5y-1\]Subtracting 2y from each side,\[\large\rm 5\lt 3y-1\]Adding 1,\[\large\rm 6\lt 3y\]Divide 3 gives us,\[\large\rm 2\lt y\]

- shreenithaa

how do u do the union sign?

- zepdrix

Again, to do it in text, you'll have to google it :) lol
In the equation tool, it's the command \cup

- shreenithaa

no i mean write it in interval notation

- zepdrix

Well we're not quite there yet :O
Both of your y values look incorrect.
The other y interval I think is \(\large\rm y\lt -3\)
That's what I'm coming up with at least, hmm

- shreenithaa

i checked and i got t right

- zepdrix

...?? 0_o
-2 and -4 are not the correct values though..

- shreenithaa

yeah -2 isnt \
just checked
forgot it was -6

- shreenithaa

-4 is right though

- zepdrix

No, neither number is correct :(
One sec..

- zepdrix

Ya in the first one, it was supposed to be -6, not 6.
So that should change it to \(\large\rm y\gt 2\)
In the second one, your -6 turned into a -8 halfway through.
So fixing that should give you \(\large\rm y\lt -3\)

- shreenithaa

yeah nevermind

- zepdrix

Hard to keep track of all these little steps :D lol

- shreenithaa

i c my mistake sorry

- shreenithaa

now finally how do u do the union thingy

- zepdrix

\(\large\rm y\lt-3 ~OR~ y\gt2\)
The word OR means union, as you said :)\[\large\rm y\lt-3 ~\cup~ y\gt2\]Let's write the y<3 as an interval.

- zepdrix

y<-3*

- shreenithaa

so the u is replaced for or?

- zepdrix

Yes :) The union symbol and the word OR mean the same thing

- zepdrix

But we have a little more to do

- shreenithaa

ooh wow does that sound easy now
what grade r u in
and state

- shreenithaa

i only need the union sign

- zepdrix

\(\large\rm y\lt-3\) can be written as \(\Large\rm \left(-\infty,-3\right)\)
-3 is the largest value this interval can have.
and every number below that should be included in the interval.
Does that make sense? :o

- zepdrix

oh you don't need the intervals? :D

- shreenithaa

nope the intervals have to be as the union sign or something like that

- shreenithaa

these are disjunctions so yeah

- shreenithaa

lol

- zepdrix

If we're using the Union symbol, we usually write the inequalities as intervals.
So for our problem,\[\large\rm y\lt-3 ~OR~ y\gt2\]We would write it as\[\large\rm (-\infty,-3)\cup(2,\infty)\]

- shreenithaa

thnx what grade r u in

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