Solve -(x-2)(-x-9)>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, - 9) \cup (2, + \infty)

Evaluate

- (x - 2) (- x - 9) > 0

Calculate

(- x + 2) (- x - 9) > 0

Change the signs on both sides of the inequality and flip the inequality sign

(x - 2) (- x - 9) < 0

Rewrite the expression

(x - 2) (- x - 9) = 0

Separate the equation into 2 possible cases

x - 2 = 0 - x - 9 = 0

Solve the equation

More Steps

x = 2 - x - 9 = 0

Solve the equation

More Steps

x = 2 x = - 9

Determine the test intervals using the critical values

x < - 9 - 9 < x < 2 x > 2

Choose a value form each interval

x_{1} = - 10 x_{2} = - 4 x_{3} = 3

To determine if x < - 9 is the solution to the inequality,test if the chosen value x = - 10 satisfies the initial inequality

More Steps

x < - 9 is the solution x_{2} = - 4 x_{3} = 3

To determine if - 9 < x < 2 is the solution to the inequality,test if the chosen value x = - 4 satisfies the initial inequality

More Steps

x < - 9 is the solution - 9 < x < 2 is not a solution x_{3} = 3

To determine if x > 2 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 9 is the solution - 9 < x < 2 is not a solution x > 2 is the solution

Solution

x \in (- \infty, - 9) \cup (2, + \infty)

Show Solution