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We are currently studying Linear Programming in school and while going through it i seem to of come across a ridiculous error. Problem is, i can't seem to find it.

Essentially there is an equation 8 - x - y >= 0 (>= signifies greater than or equal to. I'm sorry but i don't know how to replicate the symbol here) But multiplying it by -1 we get

x + y - 8 >= 0
x + y => 8
or
8 <= x + y

Instead if we add - (x + y) to the original equation you get 8 >= x + y

But, that can't be right? I always thought that mathematics was an absolute science and the end value of an equation (and inequation?) remained constant throughout, but then where did i go wrong in the above? Also if that is not the case, what is the correct way to evaluate an inequation?

Aayush Agrawal
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1 Answers1

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If you multiply an inequality with a negative number, you have to swap the sides (or change the relation: 'less than' becomes 'greater than' and vv.):

$$8 - x -y \geq 0 \Rightarrow (-1)(8 - x - y) \leq (-1) 0 \Rightarrow x + y - 8 \leq 0 $$

collapsar
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