Saturday, December 21, 2013

Solve the inequality (x+3)(2x-3)

We'll conclude that a product is negative if the factors
are of opposite sign.


There are 2 cases of
study:


1)  (2x-3) <
0


and


      (x+3) >
0


We'll solve the first inequality. For this reason, we'll
isolate 2x to the left side.


2x <
3


We'll divide by 2:


x
< 3/2


We'll solve  the 2nd
inequality:


    (x+3) >
0


We'll subtract 3 both
sides:


x > -3


The
common solution of the first system of inequalities is the interval (-3 ,
3/2).


We'll solve the second case  for the following system
of inequalities:


2)  (2x-3) >
0


and


      (x+3) <
0


2x-3 > 0


We'll add 3
both sides:


2x > 3


x
> 3/2


     (x+3) <
0


x < -3


Since there is
not a common interval to satisfy both inequalities, we don't have a solution for the 2nd
case.


So, the complete solution is the
solution from the first system of inequalities, namely the interval (-3 ,
3/2).

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