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what is jk?
ok so here we go...
we have the set up which states that only students within a certain range, can use the trombone...
so 95 is less than equal to T which is less than equal to 185..
now this next part i found on the internet...but it was suggested that i find the middle of the range which is 140, and so i subtract 140 from each part of the setup???Attachment 24548
so now i have this inequality that i need to rewrite with the use of absolute value bars, but the only problem is that i do not know how to set that up...any help would be appreciated and can you explain why i need to find the middle of the range and why is that being subtracted from either side. thanks

Re: what is jk?
we know that 95 ≤ w ≤ 185 (i am using w instead of T, to match the book).
what we want is something that looks like:
w  j ≤ k, which is the same as:
k ≤ w  j ≤ k
if we add j to everything, we get:
k + j ≤ w ≤ k + j, which is what we have:
k + j = 185
k + j = 95
let's add the two equations, to get:
k + j + k + j = 185 + 95
2j = 280
j = 140 (see where the 140 comes in?)
now we can find k:
k + j = 185
k + 140 = 185
k = 45
as a check, we verify the other equation as well:
k + j = 95
k + 140 = 95
k = 45
k = 45.
now we know that:
95 ≤ w ≤ 185 is the same condition as:
45 + 140 ≤ w ≤ 45 + 140
45 ≤ w  140 ≤ 45
w  140 ≤ 45.
it should be obvious what jk is now.

Re: what is jk?
Hello, slapmaxwell1!
Maybe a picture will clarify the situation.
. .
The middle of range is 140 pounds.
We can see that a student's weight must be
. . no more than 45 pounds away from the middle.
This can be written: .
Hence: .
Therefore: .