Question

solve 3(5t+4)<13t-10

Answer 1

I got t<-11 is that right?

Answer 2

you are correct

Answer 3

ok do I need to write it differently or just leave it like that

Answer 4

you could leave it like that or write it in set builder notation or interval notation

Answer 5

depends on how your book wants the answer

Answer 6

I think I'm supposed to use interval notation

Answer 7

ok what do you get when you convert over

Answer 8

uummm you write equal to all real number less than -11?

Answer 9

you want to describe the interval of all numbers less than -11

Answer 10

so if you wanted to described the interval from 5 to 23 (not including either endpoint), then you would write: (5, 23)

Answer 11

(0,-11) ?

Answer 12

0 is larger than -11 so that makes no sense

Answer 13

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?

Answer 14

how would I describe the interval of numbers larger than 5

Answer 15

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

\[\large\left(5,\infty \right )\]

Answer 16

does that example help?

Answer 17

so \[(-11,-\infty)\]

Answer 18

close, but the negative infinity is always on the left because it's always smaller

Answer 19

in my example, infinity is on the right since it's always larger

Answer 20

ok \[(-\infty,-11)\]

Answer 21

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

Answer 22

but that doesn't work in my case because t is less than -11

Answer 23

don't worry about (0, -11) and (-11, 0), they are just examples of what is good and bad notation for interval notation

Answer 24

ok thanks

Answer 25

the answer is \[\large\left(-\infty,-11 \right )\] and you already got that

Answer 26

np