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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