[email protected] wrote:(x^2+6x-7) / |x+4| < 0
A) -7<x<-5 and -4<x<1
B) -7<x<-5 and -4<x<0
C) -7<x<-4 and -4<x<1
D) -7<x<-6 and -4<x<1
(x+7)(x-1) / |x+4| < 0.
The CRITICAL POINTS are x=-7, x=1 and x=-4.
These are the values where (x+7)(x-1) / |x+4| = 0 or where (x+7)(x-1) / |x+4| is undefined.
To determine the ranges where (x+7)(x-1) / |x+4| < 0, test one value to the left and right of each critical point.
x<-7:
Plugging x=-8 into (x+7)(x-1) / |x+4| < 0, we get;
(-8+7)(-8-1) / |-8+4| < 0
(-1)(-9) / 4 < 0
9/4 < 0.
Doesn't work.
x<-7 is not a valid range.
-7<x<-4:
Plugging x=-5 into (x+7)(x-1) / |x+4| < 0, we get;
(-5+7)(-5-1) / |-5+4| < 0
(2)(-6) / 1 < 0
-12 < 0.
This works.
-7<x<-4 is a valid range.
-4<x<1:
Plugging x=0 into (x+7)(x-1) / |x+4| < 0, we get;
(0+7)(0-1) / |0+4| < 0
(7)(-1) / 4 < 0
-7/4 < 0.
This works.
-4<x<1 is a valid range.
x>1:
Plugging x=2 into (x+7)(x-1) / |x+4| < 0, we get;
(2+7)(2-1) / |2+4| < 0
(9)(1) / 6 < 0
3/2 < 0.
Doesn't work.
x>1 is not a valid range.
Result:
The valid ranges are -7<x<-4 and -4<x<1.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
