Question

|(8x+56)/56|>/10
I got -77 and 63 for the answers but I don't know how to put it in interval notation

Answer 1

I tried every way and it says incorrect or i have overlapping intervals

Answer 2

Do you think that it is the right answer or do you need help solving

Answer 3

is the >10 or is it really >/10

Answer 4

its > with a line under it

Answer 5

Im 90 percent sure that is the right answer

Answer 6

let me check the work first okay

Answer 7

okay

Answer 8

did you end up getting [-77,63]

Answer 9

yea

Answer 10

did you have answer chocies

Answer 11

what do you mean?

Answer 12

like is it multiple choice

Answer 13

no

Answer 14

hmm sorry i am of no help but the only choice i would think it would be was [63,infinity).
sorry

Answer 15

its okay thanks

Answer 16

Hey ms britt c:

Answer 17

Hi again!

Answer 18

\[\Large\rm \left|\frac{8x+56}{56}\right|\ge 10\]Multiply both sides by 56,\[\Large\rm \left|8x+56\right|\ge 560\]Then we end up with our two cases again when we drop the absolute bars.\[\Large\rm \cases{8x+56\ge560\\ \rm 8x+56\le-560}\]Solving for x in each case gives us:\[\Large\rm \cases{x\ge63\\ \rm x\le-77}\]So it looks like you've got the correct numbers.
Just need some help writing in this in interval notation?

Answer 19

Do you understand why the inequality flipped directions in the second case?

Answer 20

yes

Answer 21

dividing by a negative

Answer 22

x greater than or equal to 63,
So we'll have 63 and all the values larger than that heading towards positive infinity.

x less than or equal to -77,
We'll also have -77 and all the values smaller than that, heading towards negative infinity.

Answer 23

Note: ALWAYS use a round bracket for \(\Large\rm \infty\).
We don't "include" infinity in our interval since it doesn't represent an actual value.

So for our lower side we'll have: \(\Large\rm (\infty,~ -77 \)
What is different in this problem?
What type of bracket do we want on the -77?

Answer 24

]

Answer 25

Good good, I just realized I made a typo, lemme fix the -infty,\[\Large\rm (-\infty,~ -77]\]So that's one of our pieces.

Answer 26

How bout the other one, what do you think? c:

Answer 27

(inf, 63]

Answer 28

wait [63, inf)

Answer 29

Yah there we go!
We want the SMALLER number on the left since we read from left to right.\[\Large\rm [63,\infty)\]

Answer 30

How do we put them together?
Union or Intersection?

Here, I'll give you a little cheat sheet.