shreenithaa
  • shreenithaa
write the solution in interval notation using the union sign U 2y+5<5y-1 or 5y-1<3y-7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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shreenithaa
  • shreenithaa
@ganeshie8 @zepdrix
zepdrix
  • zepdrix
\[\large\rm 2y+5\lt 5y-1\]What do you get when you simplify? :)
shreenithaa
  • 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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shreenithaa
  • shreenithaa
@zepdrix
shreenithaa
  • shreenithaa
how do u write the interval notation using the union sign
zepdrix
  • 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
  • shreenithaa
how do u do the union sign?
zepdrix
  • zepdrix
Again, to do it in text, you'll have to google it :) lol In the equation tool, it's the command \cup
shreenithaa
  • shreenithaa
no i mean write it in interval notation
zepdrix
  • 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
  • shreenithaa
i checked and i got t right
zepdrix
  • zepdrix
...?? 0_o -2 and -4 are not the correct values though..
shreenithaa
  • shreenithaa
yeah -2 isnt \ just checked forgot it was -6
shreenithaa
  • shreenithaa
-4 is right though
zepdrix
  • zepdrix
No, neither number is correct :( One sec..
zepdrix
  • 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
  • shreenithaa
yeah nevermind
zepdrix
  • zepdrix
Hard to keep track of all these little steps :D lol
shreenithaa
  • shreenithaa
i c my mistake sorry
shreenithaa
  • shreenithaa
now finally how do u do the union thingy
zepdrix
  • 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
  • zepdrix
y<-3*
shreenithaa
  • shreenithaa
so the u is replaced for or?
zepdrix
  • zepdrix
Yes :) The union symbol and the word OR mean the same thing
zepdrix
  • zepdrix
But we have a little more to do
shreenithaa
  • shreenithaa
ooh wow does that sound easy now what grade r u in and state
shreenithaa
  • shreenithaa
i only need the union sign
zepdrix
  • 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
  • zepdrix
oh you don't need the intervals? :D
shreenithaa
  • shreenithaa
nope the intervals have to be as the union sign or something like that
shreenithaa
  • shreenithaa
these are disjunctions so yeah
shreenithaa
  • shreenithaa
lol
zepdrix
  • 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
  • shreenithaa
thnx what grade r u in

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