Let's solve this one component at a time
* * * * * * * * * * * * * * * * * * * * * * *⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
y < 3 y<3 is saying that yy is less than -- but not including -- 33. So we just need to convey that same information in interval notation.
First, do we use ( color(white)(.) )(.) or [ color(white)(.) ][.]? Well, we aren't including 33, so we use ( color(white)(.) )(.).
Now, what do we do with the 33? Well, are we starting at 33 or is it our end point? Are we saying that we go from 33 to infinity or from (negative) infinity to 33? In our case, we're going from infinity to 33 and 33 is our greatest value. So since we stop at 33, we put 33 last in the parentheses.
( -oo , 3 )(−∞,3)
color(white)
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Now let's do the other one
3y+4 > -53y+4>−5
first, we ought to get yy on the right side of the sign:
3y > -93y>−9
y > -3y>−3
Now we go through the same process as before:
( color(white)(.) )(.) or [ color(white)(.) ][.]?
Not including -3−3 so we'll use ( color(white)(.) )(.)
This says that yy is larger than -3−3, or that yy goes from -3−3 to infinity
( -3, oo )(−3,∞)
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Now we put these together. it's pretty simple. We just need to figure out if we use uu∪ or nn∩?
I like to remember annda∩d ( and ). Well in our case, we were told "or", so we should use uu∪
Our final answer is ( -oo , 3 ) uu ( -3, oo )(−∞,3)∪(−3,∞)