SOLUTION: Hi, How do I solve this inequality? GIven that y is always positive and z is always negative, solve 2xyz + yz > 3xyz for x Thank you

Algebra ->  Equations -> SOLUTION: Hi, How do I solve this inequality? GIven that y is always positive and z is always negative, solve 2xyz + yz > 3xyz for x Thank you      Log On


   

Question 1087856: Hi,
How do I solve this inequality?
GIven that y is always positive and z is always negative, solve 2xyz + yz > 3xyz for x
Thank you
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
yz < 0
:
-2xyz - yz > -3xyz
:
add 3xyz to both sides of >
:
xyz > yz
:
*******
x > 1
*******
:

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given 


2xyz + yz > 3xyz,    (1)
y > 0,               (2)
z < 0.               (3)


Add -3xyz to both sides of inequality (1). You will get an equivalent inequality


-xyz + yz > 0.


Factor out yz in the last inequality. You will get an equivalent inequality


yz*(-x+1) > 0.


Divide both sides by yz.  Since yz is NEGATIVE, do not forget to replace the inequality sign by the opposite.
You will get an equivalent inequality


-x + 1 < 0.


Add x to both sides.  You will get an equivalent inequality

x > 1.


It is your

Answer. x > 1.


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The other's tutor writing is incorrect.  For your safety,  do not consider it as a valid sample.

It is  invalid,  actually (and unfortunately).   Simply ignore it.