Question 463978: I need to know whether the inequality |3x-6y|< or equal to 9, lies in, out, or both in and out, of a box whose coordinates are [(1,1), (2,1), (2,2,), and (1,2)].
Please and thanks!
Answer by Edwin McCravy(20086)   (Show Source):
You can put this solution on YOUR website!
|3x-6y| ≦ 9
Factor out 3
3|x-2y| ≦ 9
Divde both sides by 3
|x-2y| ≦ 3
First we get the boundary graph:
|x-2y| = 3
x-2y = 3 and x-2y = -3
We graph those two lines
Now we use the origin (0,0) as a test point:
|x-2y| ≦ 3
|0-0y| ≦ 3
0 ≦ 3
That's true so the region that should be shaded is
the strip between the two lines, and including
the two lines as well.
Now we'll draw the box with the corners:
(1,1), (2,1), (2,2,), and (1,2)
The strip between the two parallel lines contains all of the
box, and a whole lot more too. So the answer is "both in and out".
[The upper left corner of the box (1,2) is on the boundary, but the
inequality includes its bondary.]
Edwin
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