This is a blog for my second semester pre-calculus 30s students. Have a blast!

Wednesday, March 15, 2006

Solving Absolute value & Rational Equations

So this is my first scribe duty and what your going to see won't nearly be as creative as the other posts...but i'll try my best. In today's class we learned how to solve Absolute Value & Radical equations and if your a bit lost, or didnt go to the class...hopefully this will help.

Absolute Value Eq'n

* The Absolute Value of a number can be thought of as the DISTANCE FROM ZERO on a number line.
* Any positive or negative number can have a POSITIVE DISTANCE from ZERO.

--> The absolute value of any number is:

a = a, if a<0
a = -a, if a<0

--> 5 = 5
--> -3 = 3

EX- Solve x² - 3x = -4x + 6

x² -3x = -4x + 6 x²-3x = 4x - 6
x²+x-6 = 0 x² -7x +6 = 0
(x + 3)(x - 2) = 0 (x - 6) (x - 1)

x = -3, 2 x = 6, 1

Check: (-3) : 18 = 18 (correct)
(2) : -2 = -2 (In-correct, can't be negative)
(6) : 18 = -18 ( " " " " " )
(1) : -2 = 2 (correct)

______________________________________________________________________

RATIONAL EQ'N

* A Rational Eq'n is where the variable (x) is part of the denominator of a fraction

There are 2 rules :

1) Factor
2) Find LCM (lowest common multiple) and Multiply each term by it.

Ex - Solve: 3x/x-2 = 2 + 6/x-2 LCM: x-2

3x = 2(x-2) +6
3x = 2x-4+6
x = 2 <--- Restriction "can't = 2"

And i'll give you one more example because i have to study guys ! (much needed studying time !!!!!!)

Ex. Solve. 3x/x+1 = 12/x²-1 + 2 LCM: (x-1)(x+1)
3x/x+1 = 12/(x-1)(x+1) + 2
3x(x-1) = 12 + 2(x²-1)
3x² -3x = 12 +2x² - 2
x²-3x-10 = 0
(x-5)(x+2)

Therefore x=5, -2

So that pretty much was the lesson of today...sorry if it didn't help, i tried my best to make it look good

The next scribe will be...STEVEN!

















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