Solve 12/(x^3)>4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x < 33

Alternative Form

x \in (0, 33)

Evaluate

\frac{12}{x ^{3}} > 4

Find the domain

More Steps

\frac{12}{x ^{3}} > 4, x \neq = 0

Move the expression to the left side

\frac{12}{x ^{3}} - 4 > 0

Subtract the terms

More Steps

\frac{12 - 4 x ^{3}}{x ^{3}} > 0

Set the numerator and denominator of \frac{12 - 4 x ^{3}}{x ^{3}} equal to 0 to find the values of x where sign changes may occur

12 - 4 x^{3} = 0 x^{3} = 0

Calculate

More Steps

x = 33 x^{3} = 0

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

x = 33 x = 0

Determine the test intervals using the critical values

x < 0 0 < x < 33 x > 33

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 < 33 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 < 33 is the solution x_{3} = 2

To determine if x > 33 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 < 33 is the solution x > 33 is not a solution

The original inequality is a strict inequality,so does not include the critical value ,the final solution is 0 < x < 33

0 < x < 33

Check if the solution is in the defined range

0 < x < 33, x \neq = 0

Solution

0 < x < 33

Alternative Form

x \in (0, 33)

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