Solve 2m^3 - 11m < 12m 9

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

m \in (- \infty, - \frac{238}{2}) \cup (0, \frac{238}{2})

Evaluate

2 m^{3} - 11 m < 12 m \times 9

Multiply the terms

2 m^{3} - 11 m < 108 m

Move the expression to the left side

2 m^{3} - 11 m - 108 m < 0

Subtract the terms

More Steps

2 m^{3} - 119 m < 0

Rewrite the expression

2 m^{3} - 119 m = 0

Factor the expression

m (2 m^{2} - 119) = 0

Separate the equation into 2 possible cases

m = 0 2 m^{2} - 119 = 0

Solve the equation

More Steps

m = 0 m = \frac{238}{2} m = - \frac{238}{2}

Determine the test intervals using the critical values

m < - \frac{238}{2} - \frac{238}{2} < m < 0 0 < m < \frac{238}{2} m > \frac{238}{2}

Choose a value form each interval

m_{1} = - 9 m_{2} = - 4 m_{3} = 4 m_{4} = 9

To determine if m < - \frac{238}{2} is the solution to the inequality,test if the chosen value m = - 9 satisfies the initial inequality

More Steps

m < - \frac{238}{2} is the solution m_{2} = - 4 m_{3} = 4 m_{4} = 9

To determine if - \frac{238}{2} < m < 0 is the solution to the inequality,test if the chosen value m = - 4 satisfies the initial inequality

More Steps

m < - \frac{238}{2} is the solution - \frac{238}{2} < m < 0 is not a solution m_{3} = 4 m_{4} = 9

To determine if 0 < m < \frac{238}{2} is the solution to the inequality,test if the chosen value m = 4 satisfies the initial inequality

More Steps

m < - \frac{238}{2} is the solution - \frac{238}{2} < m < 0 is not a solution 0 < m < \frac{238}{2} is the solution m_{4} = 9

To determine if m > \frac{238}{2} is the solution to the inequality,test if the chosen value m = 9 satisfies the initial inequality

More Steps

m < - \frac{238}{2} is the solution - \frac{238}{2} < m < 0 is not a solution 0 < m < \frac{238}{2} is the solution m > \frac{238}{2} is not a solution

Solution

m \in (- \infty, - \frac{238}{2}) \cup (0, \frac{238}{2})

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