Solve -3x^28x < (x - 1) (x^2)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x > \frac{1}{25}

Alternative Form

x \in (\frac{1}{25}, + \infty)

Evaluate

- 3 x^{2} \times 8 x < (x - 1) x^{2}

Multiply

More Steps

- 24 x^{3} < (x - 1) x^{2}

Multiply the terms

- 24 x^{3} < x^{2} (x - 1)

Move the expression to the left side

- 24 x^{3} - x^{2} (x - 1) < 0

Subtract the terms

More Steps

- 25 x^{3} + x^{2} < 0

Rewrite the expression

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

Factor the expression

x^{2} (- 25 x + 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 - 25 x + 1 = 0

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

x = 0 - 25 x + 1 = 0

Solve the equation

More Steps

x = 0 x = \frac{1}{25}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{1}{25} x > \frac{1}{25}

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{1}{50} x_{3} = 1

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}{50} x_{3} = 1

To determine if 0 < x < \frac{1}{25} is the solution to the inequality,test if the chosen value x = \frac{1}{50} satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{1}{25} is not a solution x_{3} = 1

To determine if x > \frac{1}{25} 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{1}{25} is not a solution x > \frac{1}{25} is the solution

Solution

x > \frac{1}{25}

Alternative Form

x \in (\frac{1}{25}, + \infty)

Show Solution