Solve 3x^3-2x^2>0

Question

Solve the inequality

x > \frac{2}{3}

Alternative Form

x \in (\frac{2}{3}, + \infty)

Evaluate

3 x^{3} - 2 x^{2} > 0

Rewrite the expression

3 x^{3} - 2 x^{2} = 0

Factor the expression

x^{2} (3 x - 2) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 x - 2 = 0

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

x = 0 3 x - 2 = 0

Solve the equation

More Steps

x = 0 x = \frac{2}{3}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{2}{3} x > \frac{2}{3}

Choose a value form each interval

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

To determine if 0 < x < \frac{2}{3} is the solution to the inequality,test if the chosen value x = \frac{1}{3} satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{2}{3} is not a solution x_{3} = 2

To determine if x > \frac{2}{3} 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{2}{3} is not a solution x > \frac{2}{3} is the solution

Solution

x > \frac{2}{3}

Alternative Form

x \in (\frac{2}{3}, + \infty)

Show Solution