Solve 2/(x^3)>=5 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < x \leq \frac{3 50}{5}

Alternative Form

x \in (0, \frac{3 50}{5}]

Evaluate

\frac{2}{x ^{3}} \geq 5

Find the domain

More Steps

\frac{2}{x ^{3}} \geq 5, x \neq = 0

Move the expression to the left side

\frac{2}{x ^{3}} - 5 \geq 0

Subtract the terms

More Steps

\frac{2 - 5 x ^{3}}{x ^{3}} \geq 0

Set the numerator and denominator of \frac{2 - 5 x ^{3}}{x ^{3}} equal to 0 to find the values of x where sign changes may occur

2 - 5 x^{3} = 0 x^{3} = 0

Calculate

More Steps

x = \frac{3 50}{5} x^{3} = 0

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

x = \frac{3 50}{5} x = 0

Determine the test intervals using the critical values

x < 0 0 < x < \frac{3 50}{5} x > \frac{3 50}{5}

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{3 50}{10} 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} = \frac{3 50}{10} x_{3} = 2

To determine if 0 < x < \frac{3 50}{5} is the solution to the inequality,test if the chosen value x = \frac{3 50}{10} satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < \frac{3 50}{5} is the solution x_{3} = 2

To determine if x > \frac{3 50}{5} 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{3 50}{5} is the solution x > \frac{3 50}{5} is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

0 < x \leq \frac{3 50}{5} is the solution

The final solution of the original inequality is 0 < x \leq \frac{3 50}{5}

0 < x \leq \frac{3 50}{5}

Check if the solution is in the defined range

0 < x \leq \frac{3 50}{5}, x \neq = 0

Solution

0 < x \leq \frac{3 50}{5}

Alternative Form

x \in (0, \frac{3 50}{5}]

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