Linear equation solutions graphically

[fredx]

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 => [tex]x_{1 }[/tex] = 1
x-2 = 0 => [tex]x_{2 }[/tex] = 2
x-3 = 0 => [tex]x_{3 }[/tex] = 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.

[Baltuilhe]

Good afternoon!!

Follow the drawing

inequacao.jpg (46.07 KiB) Viewed 496 times

[fredx]

Good afternoon!!

Follow the drawing

Thanks a lot!

[HallsofIvy]

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.