Yesterday and Todays blog!
Man I still don't see why I gotta blog twice. -_-'
" RATIONAL INEQUALITIES "
STEPS TO SOLVING THESE ..
x - 1
--------- <>
(x-2)(x+3)
Because the expression is LESS THAN 0 then you are looking for a negative solution(s).
STEP 1:
FACTOR NUMERATOR + DENOMINATOR..
(In this question Mrs.Ingram kindly provided you with, it is already factored)
OMG WHY IS THIS COMPUTER BEING SO SLOW.
STEP 2:
Determine the CRITICAL NUMBERS .. WOW THIS COMPUTER. !@#%@$^
What are critical numbers? Same as restricted values. What will make the denominator zero.
But now including the numerator.
SO THE CRITICAL NUMBERS ARE ..
(2, -3, 1)
STEP 3:
Place the critical numbers on a number line.
OKAY.. SO NOT ONLY THE COMPUTER IS SUCKING. BUT SO ARE MY QUALITIES OF PICTURES. whatever.
I know its beautiful, because it was made in 5 hours.
p.s. don't even try reading the little jibberish. dont even look like english haha. but if you somehow manage and tell me what it says, amazing, i'll give ya a cookie.
REMEMBER that <> are OPEN CIRCLES. and LESS THAN + UNDERSCORE ( <_>_ ) .. (Greater than or equal to, less than or equal to) are CLOSED CIRCLES.
Step 4:
Test each interval. Doing this by taking ANY number ( yes even gajabebebillion ) EXCEPT the open circled numbers. So taken from the crusty image I provided you, anything from -oo to -4 .. Then taking those numbers and plugging them into the expression ..
x - 1
------
(x-2)(x+3)
so lets choose -11, because everyone loves it and its beautiful and its special and its cool and the best kk.
SO .. (-11) - 1 = -12
(-11-2)(-11+3) = -13(-8) is something something.. BUT THE ANSWER IS POSITIVE and thats all that matters.
because now it would be NEGATIVE / POSITIVE .. which is NEGATIVE.. Still with me?
Now knowing that the WHOLE region from -oo to -3 IS NEGATIVE, we still have to find the other regions, using the same steps of choosing and subsituting.
Because I'm nice and lazy, I'm just going to tell you signs of each region.
(-oo, -3) = NEGATIVE
(-3, 1) = POSITIVE
(1, 2) = NEGATIVE
(2, oo) = POSITIVE
Now because we know what solution(s) we are looking for, we pretty much choose which region is the correct one.
Therefore the solution is ..
(-oo, -3) AND (1, 2)
WOOHOO..
NEXT! .. This one had no title. But I'm going to guess it is ..
" ABSOLUTE VALUE INEQUALITIES " (on the calcul
ator it says "ABS(" LOLOL .. uh lots of laughter )
ator it says "ABS(" LOLOL .. uh lots of laughter )Okay yet another crappy image. But you gotta hand it to me, its still beautiful. Anyways the text on the left shows ..
" Y = x " .. and the right says..
"Okay this is your basic everyday " Y = X " graph. Have you ever wondered what would happen if the equation was
"Y = x" ? .. Yeah me neither ha. But if it was, the VALUE of X would always be positive, thus forming a V..
Alright now .. solving absolute inequalities are as easy as wrestling a great white shark.
GIVEN THIS EQUATION MRS.INGRAM, AGAIN, KINDLY PROVIDES.
X - 2 <= 5
Two ways of solving ABSOLUTE VALUES.
FIRST WAY)
TREAT IT WAS AN EQUATION. so ..
1) X - 2 <= 5
2) x <= 7
SECOND WAY)
ADD A NEGATIVE TO THE SIDE WITH X
1) -(X - 2) <= 5
2) -X+2 <= 5
3) -X <= 3
4) X >= -3
Now using the number line, plugging the values 7 and -3 in. Remember, closed circles.
because X <= 7 and X >= -3, then region is in the middle!
The interval would be ..
-3 <= x <= 7 ( Justice says its ugly so .. )
[-3, 7] CLOSED BRACKETS. OR SQUARE WHATEVER YOU CALL IT.
If you are given a question such as..
X/2 + 1 <>
YES EXACT ..
" ha ha, you can't do that, nice try. you can't mess me up like that. oh come on. I know better than that. Now go give Elven some cookies "
... AND CUUT!
yes.. 2 blogs. pretty deadly = .. NOW FOR MY FAVOURITE PART. THE CHOOSING THE NEXT BLOGGER THINGYMAJIG
mmm. its of course.. the one and obvious
ROXXANE .. YUMANG ..
* DUN DUN DUNN
hA! i hope she doesn't see this so that she misses her blog and has to do 2 or 3 and suffer like i did.
yea anyways. this is brought to you by Elven. Please edit if you see mistakes. Thanks!
mm im hungry
posted by Eleven @ 8:05 PM
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