Question 1148538: Given that -4 ≤ x ≤ -2 and 2 ≤ y ≤ 4, what is the largest possible value of (x+y)/x?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
This problem is VERY SIMPLE.
Moreover, it is EXTREMELY SIMPLE, and I will show it to you right now.
Our function is  = 1 +  . (1)
The given area is the square ABCD in quadrant QII with the vertices
A= (-4,2), B= (-2,2), C= (-2,4), D= (-4,4).
The given function, OBVIOUSLY, adds the ratio to the value of 1.
But this ratio is negative in QII.
Thus the function (1), actually, adds NEGATIVE amount to 1.
- When the function (1) will have the largest value ?
- OBVIOUSLY, when this negative addend will have minimal absolute value.
- When this addend will have minimal absolute value ?
- OBVIOUSLY, when positive "y" is minimal and negative "x" has maximal absolute value.
- Now, what is the point of the given square, where positive "y" is minimal and negative "x" has maximal absolute value ?
- OBVIOUSLY, this point is A= (-4,2).
Then the larges possible value of the function is  =  = 1 -  = . ANSWER
Solved, explained, answered and completed.
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O-o-o, tutor @greenestamps successfully retold my solution to this problem !
Congratulations (!) (!)
It seems, you invented the new way to increase the number of your posts by retelling my solutions !
Answer by greenestamps(13200)  (Show Source):
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