SOLUTION: What is the least value of y that satisfies the following inequality? |4+x|+|5+y|≤100

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Question 257610: What is the least value of y that satisfies the following inequality?
|4+x|+|5+y|≤100
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
WIth these absolute values we must start with 4 inequalities. here are the four:
(i) %284%2Bx%29+%2B+%285%2By%29+%3C=+100
(ii) %284%2Bx%29+-+%285%2By%29+%3C=100
(iii)-%284%2Bx%29+%2B+%285%2By%29+%3C=100
(iv) -%284%2Bx%29+-+%285%2By%29+%3C=100
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we can solve each of these for y as
(i) becomes (v) y+%3C=+91-x
(ii) becomes (vi) y+%3E=+x-101
(iii) becomes (vii) y%3C=+x+%2B+99
(iv) becomes (viii) y%3E=+-x+-109
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Graphing them creates a quadrilateral. We now graph these and look for the minimum y crossing points. This occurs when (vi) crosses over (viii). We get
y+%3E=+x-101
y%3E=+-x+-109
adding down, the x's drop out and we get
2y+%3E=+-210
and then
y+%3E=+-105
So, the minimum value of y is -105.