# 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

Posts: 2
Joined: Wed Jan 13, 2021 10:26 am
Reputation: 0

### Re: Linear equation solutions graphically

Good afternoon!!

Follow the drawing  inequacao.jpg (46.07 KiB) Viewed 59 times

Baltuilhe

Posts: 74
Joined: Fri Dec 14, 2018 3:55 pm
Reputation: 49

### Re: Linear equation solutions graphically

Baltuilhe wrote:Good afternoon!!

Follow the drawing Thanks a lot!

fredx

Posts: 2
Joined: Wed Jan 13, 2021 10:26 am
Reputation: 0

### 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

Posts: 318
Joined: Sat Mar 02, 2019 9:45 am
Reputation: 108