Solve 11x>6x^32 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, - \frac{33}{6}) \cup (0, \frac{33}{6})

Evaluate

11 x > 6 x^{3} \times 2

Multiply the terms

11 x > 12 x^{3}

Move the expression to the left side

11 x - 12 x^{3} > 0

Rewrite the expression

11 x - 12 x^{3} = 0

Factor the expression

x (11 - 12 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 11 - 12 x^{2} = 0

Solve the equation

More Steps

x = 0 x = \frac{33}{6} x = - \frac{33}{6}

Determine the test intervals using the critical values

x < - \frac{33}{6} - \frac{33}{6} < x < 0 0 < x < \frac{33}{6} x > \frac{33}{6}

Choose a value form each interval

x_{1} = - 2 x_{2} = - \frac{33}{12} x_{3} = \frac{33}{12} x_{4} = 2

To determine if x < - \frac{33}{6} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{33}{6} is the solution x_{2} = - \frac{33}{12} x_{3} = \frac{33}{12} x_{4} = 2

To determine if - \frac{33}{6} < x < 0 is the solution to the inequality,test if the chosen value x = - \frac{33}{12} satisfies the initial inequality

More Steps

x < - \frac{33}{6} is the solution - \frac{33}{6} < x < 0 is not a solution x_{3} = \frac{33}{12} x_{4} = 2

To determine if 0 < x < \frac{33}{6} is the solution to the inequality,test if the chosen value x = \frac{33}{12} satisfies the initial inequality

More Steps

x < - \frac{33}{6} is the solution - \frac{33}{6} < x < 0 is not a solution 0 < x < \frac{33}{6} is the solution x_{4} = 2

To determine if x > \frac{33}{6} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{33}{6} is the solution - \frac{33}{6} < x < 0 is not a solution 0 < x < \frac{33}{6} is the solution x > \frac{33}{6} is not a solution

Solution

x \in (- \infty, - \frac{33}{6}) \cup (0, \frac{33}{6})

Show Solution