For what x the inequality is true 2(x-1/2)(x+2)<0
Solution
We\'ll divide both sides by 2:
Since the value is positive, teh inequality still holds:
(x - 1/2)(x+2)<0
We\'ll conclude that a product is negative if the factors are of opposite sign.
There are 2 cases of study:
1) (x - 1/2) < 0
and
(x+2) > 0
We\'ll solve the first inequality. For this reason, we\'ll isolate x to the left side.
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 system of inequalities:
2) (x-1/2) > 0
and
(x+2) < 0
x-1/2 > 0
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)..
For what x the inequality is true 2(x-12)(x+2)0SolutionWel.pdf
1. For what x the inequality is true 2(x-1/2)(x+2)<0
Solution
We'll divide both sides by 2:
Since the value is positive, teh inequality still holds:
(x - 1/2)(x+2)<0
We'll conclude that a product is negative if the factors are of opposite sign.
There are 2 cases of study:
1) (x - 1/2) < 0
and
(x+2) > 0
We'll solve the first inequality. For this reason, we'll isolate x to the left side.
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 system of inequalities:
2) (x-1/2) > 0
and
(x+2) < 0
x-1/2 > 0
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).
