Thread: 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???

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

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.

Hello, slapmaxwell1!

Students are allowed to use the trampoline if they weigh from 95 to 185 pounds.
Express this restriction in the form
where is a student's weight, and and are constants.
What is ?

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: .