Question

How the heck do I write a set builder and interval out of 6-8(y+3)+5y>(2y-5)+13?
once I worked it out I got y<-6m whats my next step?

Answer 1

where did the m come from in your answer?

Answer 2

thats a typo, I'm sorry.

Answer 3

y<-6

Answer 4

\[let s = \left\{ y: y<-6 \right\}\]

Answer 5

in set builder, then the interval \[y \in \left( -6, -\infty \right)\]

Answer 6

so how do I know where to put the infinity sign?

Answer 7

oh wait i miss typed that, the -6 and - infinity shud be swapped. sorry

Answer 8

the smaller value should always be on the left by convention since the interval starts at the left hand value and goes up to the right hand value

Answer 9

so when do I use that squiggly line, and bracets instead of perenthisis?

Answer 10

round brackets mean the endpoints arent in the interval and square brackets mean they are included

Answer 11

so whats the interval to this specific one? \[\xi x-6\]

Answer 12

im not sure i understand your notation, what does the lowercase delta stand for?

Answer 13

Our professor was asking for some squiggly line for example:

8-6(x-3)>-4x+12
Solution: x<7
Set Builder Notation:\[\xi x-1+<7\xi\]
Interval Notation: (-\[\infty , 5/2]\]

Answer 14

I'm sorry the interval notation is actually 7 not 5/2, but do you see what I mean?

Answer 15

maybe its just the name he is using but in any book i have ever seen set builder means { } and u state the conditions for membership of the set in the brackets

Answer 16

yes, maybe it is {

Answer 17

so to graph y<-6 it would be
<_______O
I I I I I I I I I I
-6