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I'm getting mad after noticing an anbiguous case in a inequality.

The track is: -3x+8<0

So the first step is: -3x<-8

But now, should I do 3x>8 or x<-8/-3?

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2 Answers 2

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You are on the right track. When you multiply both sides of an inequality by a negative number, you need to reverse the sign. $-3x<-8\implies(-1)(-3x)>(-1)(-8)\implies3x>8\implies\boxed{x>8/3}$.

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    $\begingroup$ When you multiply by a negative number, that is. $\endgroup$
    – amd
    Sep 29, 2015 at 19:10
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Here's another approach $$-3x+8\lt 0$$ $$8\lt 3x$$ $$\frac83\lt x$$ There's nothing wrong with having $x$ on the right-hand side.

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