Linear equation solutions graphically

Linear, quadratic, module, parametric equations

Linear equation solutions graphically

Postby fredx » Wed Jan 13, 2021 10:37 am

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":

Image

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?

Image

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

Postby Baltuilhe » Wed Jan 13, 2021 12:18 pm

Good afternoon!!

Follow the drawing :)
inequacao.jpg
inequacao.jpg (46.07 KiB) Viewed 82 times

Baltuilhe
 
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Re: Linear equation solutions graphically

Postby fredx » Wed Jan 13, 2021 12:54 pm

Baltuilhe wrote:Good afternoon!!

Follow the drawing :)


Thanks a lot!

fredx
 
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Re: Linear equation solutions graphically

Postby HallsofIvy » Thu Jan 14, 2021 5:58 pm

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.

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