Wednesday, April 25, 2007

InEqualities



Okay, today we learned about Inequalities. But First!



Here are somethings that you should know in this concept.








Know those signs!

Okay, now that you know those you can learn the lesson that was taught today.

Steps to Solving Inequalities (Graphically).


1.Graph the line that will represent the boundry line.

If the sign is > or <>
If the sign is >= or <= then the boundry line is solid.

[Sorry i dont know how to make that character on the key board and i was not gonna make some images just for that. Sorry!]


2.Test one point on each side of boundry to find area that fits the inequalitie.


Sounds confusing eh? Well thats why we have...

~~~~~~~~~~Examples~~~~~~~~~~


1. y > -2x + 4

**Note about Graphing ===> Make sure the equation(s) are in y = mx + b Form.**






Once you have your graph you much choice a point on either side of the line of boundry. Any point will be fine, just choose one. For our lesson we have choosen (10, 10) and (0, 0)

The math:

(10, 10)


10> -2(10) + 4

10> -20 + 4

10> -16

Works!



(0, 0)


0> -2(0) + 4

0> 0 + 4

0 > 4


Doesnt Work!


Tip from Mrs. Ingram: Try to use the origin if possible. It will make the math much easier for yourslef.


You really only need to do one side when solving inequalites. If one doesnt work then the inequalite is on the other side!

~~~~~~~~~~Intersections~~~~~~~~~~



I'll explain as i go along.



x + y > 6 and 2x-2y<>


Make the equations into y = mx + b








You see that?! If you divide your multiply both sides by a negative value then the sign changes! Either from Greater than to Less than or Vice versa.




Once you do that you can graph it. And pick two points on each side of both lines to fine the inequalitie.




0 > 0 + 6

0 > 6
Wont Work



0 > 0 -5/2

0 > -5/2
Work



After you do that shade the side where the inequalitie is found. Do this for both Equations. After you will have something that looks like this.




Pretty crappy graph dont you think? Oh well thats not it. The red area is where the 2x - 2y <> 's inequalite area nd the blue is where the x + y > 6 's inequalites are. What you need to know is the purple area(both area's overlap). Thats where both inequalites of both equations are. Since the question says

2x - 2y and x + y > 6
The areas that overlap is the answer.


That was confusing. A little word like "And" can make such a difference. What about "or" There's a solution for that to!


I'll skip all the algebra and stuff. By now you should know how it works, if you dont...then i dont know. Just remember that when the you multiply or divide by a negative then the sign ( <> ) changes. :P


x - 2y <5 color="#000000">.This will look like that when you do the algebra. y > x/2 - 5/2

2x + y > 3 .This will look like that when you do the algebra. y > -2x + 3


0 > 0 - 5/2

0 > -5/2

Works.


0 > 0 + 3

0 > 3

Wont Work.


Your Graph will look like...


Again i know that sucks, alot. But just read this and find out about those little words. "Or" Refers to the sides of the equations with the inequalities, not just where they meet up. Everything in the blue Boundry is the inequalitie.
Arg! I made the lines solid. You should know that the boundry lines should be dashed. I'm just to lazy to do anymore work.
We have homework.
ex. 27 1-8
Next scribe will be...Lawrence

posted by Saromo, Paulo @ 4:58 PM

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