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

1. shreenithaa

@ganeshie8 @zepdrix

2. zepdrix

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

3. 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

4. shreenithaa

@zepdrix

5. shreenithaa

how do u write the interval notation using the union sign

6. 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,$\large\rm 2\lt y$

7. shreenithaa

how do u do the union sign?

8. zepdrix

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

9. shreenithaa

no i mean write it in interval notation

10. 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

11. shreenithaa

i checked and i got t right

12. zepdrix

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

13. shreenithaa

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

14. shreenithaa

-4 is right though

15. zepdrix

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

16. 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 $$\large\rm y\lt -3$$

17. shreenithaa

yeah nevermind

18. zepdrix

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

19. shreenithaa

i c my mistake sorry

20. shreenithaa

now finally how do u do the union thingy

21. 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.

22. zepdrix

y<-3*

23. shreenithaa

so the u is replaced for or?

24. zepdrix

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

25. zepdrix

But we have a little more to do

26. shreenithaa

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

27. shreenithaa

i only need the union sign

28. 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

29. zepdrix

oh you don't need the intervals? :D

30. shreenithaa

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

31. shreenithaa

these are disjunctions so yeah

32. shreenithaa

lol

33. 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$\large\rm (-\infty,-3)\cup(2,\infty)$

34. shreenithaa

thnx what grade r u in