Solve the inequality (2x-1)(x+2)

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

There are 2 caes of
study:

1)  (2x-1) <
0

and

      (x+2) >
0

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

2x <
1

We'll divide by 2:

x
< 1/2

We'll solve  the 2nd
inequality:

    (x+2) >
0

We'll subtract 2 both
sides:

x > -2

The
common solution of the first system of inequalities is the interval (-2 ,
1/2).

We'll solve the second systemof
inequalities:

2)  (2x-1) >
0

and

      (x+2) <
0

2x-1 > 0

We'll add 1
both sides:

2x > 1

x
> 1/2

     (x+2) <
0

x < -2

Since we don't
have a common interval to satisy 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 (-2 ,
1/2).