Solve (x^2)(x-7)>0

Evaluate

x^{2} (x - 7) > 0

Rewrite the expression

x^{2} (x - 7) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x - 7 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 7 = 0

Solve the equation

More Steps

x = 0 x = 7

Determine the test intervals using the critical values

x < 0 0 < x < 7 x > 7

Choose a value form each interval

x_{1} = - 1 x_{2} = 4 x_{3} = 8

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is not a solution x_{2} = 4 x_{3} = 8

To determine if 0 < x < 7 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 7 is not a solution x_{3} = 8

To determine if x > 7 is the solution to the inequality,test if the chosen value x = 8 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 7 is not a solution x > 7 is the solution

Solution

x > 7

Alternative Form

x \in (7, + \infty)

Solve the inequality