Solve 7/2*(x^3)>3x^4

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < \frac{7}{6}

Alternative Form

x \in (0, \frac{7}{6})

Evaluate

\frac{7}{2} x^{3} > 3 x^{4}

Move the expression to the left side

\frac{7}{2} x^{3} - 3 x^{4} > 0

Rewrite the expression

\frac{7}{2} x^{3} - 3 x^{4} = 0

Factor the expression

x^{3} (\frac{7}{2} - 3 x) = 0

Separate the equation into 2 possible cases

x^{3} = 0 \frac{7}{2} - 3 x = 0

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

x = 0 \frac{7}{2} - 3 x = 0

Solve the equation

More Steps

x = 0 x = \frac{7}{6}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{7}{6} x > \frac{7}{6}

Choose a value form each interval

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

To determine if 0 < x < \frac{7}{6} 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{7}{6} is the solution x_{3} = 2

To determine if x > \frac{7}{6} 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{7}{6} is the solution x > \frac{7}{6} is not a solution

Solution

0 < x < \frac{7}{6}

Alternative Form

x \in (0, \frac{7}{6})

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