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Question 35059: Hello,
My name is Kristin and my time for the college placement exam is approaching and I need help!!!!!so please help
THE INEQUALITY X^2-14X>15 IS EQUIVALENT TO:
A. -3< X <5
B. -1< X <15
C, 3< X <5
D. X< -1 OR X >15
E. X< 3 OR X >5
I believe this is setup like x^2-14x >15= x^-14x-15 >0. then (x+1)(x-15)>0= x+1 >0 & x-15 >0. This is where I get confused after this point. I think the ans is B. because according to the two outcomes, you know w/ x+1 has to be greater than 0, which -1 isn't greater than 0. Also w/ x-15 has to be greater than 0 as well (i'm confused here)
THANK YOU IN ADVANCE,
KRISTIN
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! HAPPY TO SEE YOUR SINCERE DESIRE TO LEARN.YOU JUST NEED TO CLEAR FEW APPREHENSIONS AS YOU HAVE CLEARLY IDENTIFIED.SEE MY COMMENTS BELOW...
My name is Kristin and my time for the college placement exam is approaching and I need help!!!!!so please help
THE INEQUALITY X^2-14X>15 IS EQUIVALENT TO:
A. -3< X <5
B. -1< X <15
C, 3< X <5
D. X< -1 OR X >15
E. X< 3 OR X >5
I believe this is setup like x^2-14x >15
GOOD
= x^-14x-15 >0.
VERY GOOD
then (x+1)(x-15)>0
EXCELLENT
= x+1 >0 & x-15 >0.
NO HERE YOU ARE IN A LITTLE CONFUSION.WELL FOLLOW THIS LOGIC AND METHOD TO FREE YOUR BRAIN PERMANENTLY FROM THIS DILEMMA..
1.PRODUCT OF 2 FACTORS IS TO BE >0....THAT IS POSITIVE
2.HENCE EITHER BOTH FACTORS SHOULD BE POSITIVE OR BOTH SHOULD BE NEGATIVE
3.SO CASE 1.....BOTH POSITIVE...THAT IS X+1>0...OR....X>-1...AND X-15>0
...OR..X>15....OBVIOULY IF X>15 ,IT WILL BE>-1..SO HERE WE GET THE ANSWER AS X>15
4.NOW ON TO CASE 2...BOTH NEGATIVE..THAT IS ...X+1<0..OR..X<-1..AND...X-15<0...OR...X<15...HERE OBVIOUSLY X<-1 IS OVER RIDING SO FROM HERE WE GET X<-1...
NOW WE HAVE TO COMBINE BOTH AND SAY X>15 OR X<-1
THERE IS AN EASY WAY OF DOING THIS AS A ROUTINE...IT APPLIES FOR ANY NUMBER OF FACTORS THOUGH WE HAVE HERE ONLY 2 FACTORS...PRODUCT COULD BE POSITIVE OR NEGATIVE...
WRITE THE FACTORS IN INCREASING ORDER OF X AS YOU FOUND
(X+1)(X-15).............
PLOT THE VALUES OF X ON A NUMBER LINE IN INCREASING ORDER
NUMBER LINE.....-5.....-1....0......1.....5......10.....15....20...ETC
--------------------------------------------------------------------------------
X=.....................-1................................15.........
NOW START FROM RIGHT MOST NUMBER ON THE LINE ..IT IS X=15...HENCE WRITE IF X>15 PRODUCT IS POSITIVE....
NOW GO TOWARDS LEFT...WE FIND NEXT X=-1.......HENCE WRITE.....BETWEEN THESE 2 VALUES OF X ..THE PRODUCT IS NEGATIVE....
NOW GO FURTHER LEFT...WE FIND X<-1....HENCE WRITE IN THIS ZONE PRODUCT IS POSITIVE.....
THIS IS THE METHOD FO ANY NUMBER OF FACTORS.
1.PRODUCT IS POSITIVE BEYOND RIGHTMOST BOUNDARY VALUE OF X OR IN THE RIGHT MOST ZONE
2.THEN GO LEFT WARD AND PRODUCT BECOMES ALTERNATELY NEGATIVE ...POSITIVE...NEGATIVE..ETC...TILL YOU CROSS THE LAST BOUNDARY VALUE OF X
This is where I get confused after this point. I think the ans is B. because according to the two outcomes, you know w/ x+1 has to be greater than 0, which -1 isn't greater than 0. Also w/ x-15 has to be greater than 0 as well (i'm confused here)
THANK YOU IN ADVANCE,
KRISTIN
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