Linear equation solutions graphically

Linear equation solutions graphically

Hello!
I have a simple equation: (x-1) (x-2) (3-x) < 0
I need to give a graphical solution.

First I find the zero points:
x-1 = 0 => $$x_{1 }$$ = 1
x-2 = 0 => $$x_{2 }$$ = 2
x-3 = 0 => $$x_{3 }$$ = 3

Then I add those points to the "number axis":

Then I need to decide whether I start drawing the line from positive side (top of x-axis) or from negative.
The general rule is to start from top. But this does not give the right answer.
How to decide from where to start drawing the line?

The answer should be marked below the x-axis, because the initial function f(x) < 0 is negative.
fredx

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Re: Linear equation solutions graphically

Good afternoon!!

inequacao.jpg (46.07 KiB) Viewed 82 times

Baltuilhe

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Re: Linear equation solutions graphically

Baltuilhe wrote:Good afternoon!!

Thanks a lot!

fredx

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Re: Linear equation solutions graphically

Another way of looking at it:
If x> 3 then x- 1 and x- 2 are positive but 3- x is negative so (x-1)(x-3)(3-x) is "++-" and is negative. Each time x crosses one of those points, x= 3, x= 2, x= 1 the sign changes.

HallsofIvy

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