yumi2012 wrote:If 4/x <-1/3, what is the possible range of values for x?
4/x < -1/3
12/x < -1.
When an inequality involves negative values, many students struggle with putting the <> in the right direction.
Below is a way to avoid the issue.
12/x < -1 implies that x≠0.
Since x is NONZERO, x²>0.
Thus, we can safely multiply each side by x²:
12/x * x² < -1 * x²
12x < -x²
x² + 12x < 0
x(x+12) < 0.
The CRITICAL POINTS are where the lefthand side is EQUAL TO 0: x=0 and x=-12.
To determine where x(x+12) < 0, test one value to the LEFT AND RIGHT OF EACH CRITICAL POINT.
x<-12:
If we plug x=-13 into x(x+12) < 0, we get:
-13(-13+12) < 0
13<0.
Doesn't work.
x < -12 is not a viable range.
-12<x<0:
If we plug x=-1 into x(x+12) < 0, we get:
-1(-1+12) < 0
-11<0.
This works.
-12 < x < 0 is a viable range.
x>0:
If we plug x=1 into x(x+12) < 0, we get:
1(1+12) < 0
13<0.
Doesn't work.
x > 0 is not a viable range.
The only viable range is -12 < x < 0.
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
