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I got t<-11 is that right?
you are correct
ok do I need to write it differently or just leave it like that
you could leave it like that or write it in set builder notation or interval notation
depends on how your book wants the answer
I think I'm supposed to use interval notation
ok what do you get when you convert over
uummm you write equal to all real number less than -11?
you want to describe the interval of all numbers less than -11
so if you wanted to described the interval from 5 to 23 (not including either endpoint), then you would write: (5, 23)
0 is larger than -11 so that makes no sense
I dont know then because I know its less than -11 but I dont have a number that its greater than...so do I just leave it open ended?
how would I describe the interval of numbers larger than 5
you would do something like 5, 6, 7, 8, ... so (5, 7) is one interval...but leaves out numbers like 8, 9, 10, etc (5, 23) is another interval, but numbers like 30, 40, 50 are left out this interval is open ended because there are infinitely many numbers that are greater than 5 so you would write \[\large\left(5,\infty \right )\]
does that example help?
close, but the negative infinity is always on the left because it's always smaller
in my example, infinity is on the right since it's always larger
good, remember you're reading this from left to right (smaller to bigger) so that's why (0, -11) doesn't make any sense...however (-11, 0) does make sense
but that doesn't work in my case because t is less than -11
don't worry about (0, -11) and (-11, 0), they are just examples of what is good and bad notation for interval notation
the answer is \[\large\left(-\infty,-11 \right )\] and you already got that