Solve 5x x^2 > 100

Evaluate

5 x \times x^{2} > 100

Multiply

More Steps

5 x^{3} > 100

Move the expression to the left side

5 x^{3} - 100 > 0

Rewrite the expression

5 x^{3} - 100 = 0

Move the constant to the right-hand side and change its sign

5 x^{3} = 0 + 100

Removing 0 doesn't change the value,so remove it from the expression

5 x^{3} = 100

Divide both sides

\frac{5 x ^{3}}{5} = \frac{100}{5}

Divide the numbers

x^{3} = \frac{100}{5}

Divide the numbers

More Steps

x^{3} = 20

Take the 3 -th root on both sides of the equation

3 x^{3} = 320

Calculate

x = 320

Determine the test intervals using the critical values

x < 320 x > 320

Choose a value form each interval

x_{1} = 2 x_{2} = 4

To determine if x < 320 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 320 is not a solution x_{2} = 4

To determine if x > 320 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 320 is not a solution x > 320 is the solution

Solution

x > 320

Alternative Form

x \in (320, + \infty)

Solve the inequality