Solve the inequality 2x1x2 2 The common solution of the firs

Solve the inequality (2x-1)(x+2)<0

Solution

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).