Solve 9x > 5(x^4)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < \frac{3 225}{5}

Alternative Form

x \in (0, \frac{3 225}{5})

Evaluate

9 x > 5 x^{4}

Move the expression to the left side

9 x - 5 x^{4} > 0

Rewrite the expression

9 x - 5 x^{4} = 0

Factor the expression

x (9 - 5 x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 9 - 5 x^{3} = 0

Solve the equation

More Steps

x = 0 x = \frac{3 225}{5}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{3 225}{5} x > \frac{3 225}{5}

Choose a value form each interval

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

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} = 1 x_{3} = 2

To determine if 0 < x < \frac{3 225}{5} 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 0 < x < \frac{3 225}{5} is the solution x_{3} = 2

To determine if x > \frac{3 225}{5} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{3 225}{5} is the solution x > \frac{3 225}{5} is not a solution

Solution

0 < x < \frac{3 225}{5}

Alternative Form

x \in (0, \frac{3 225}{5})

Show Solution