Solve 4f^6 < 30 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for f

- \frac{6 480}{2} < f < \frac{6 480}{2}

Alternative Form

f \in (- \frac{6 480}{2}, \frac{6 480}{2})

Evaluate

4 f^{6} < 30

Move the expression to the left side

4 f^{6} - 30 < 0

Rewrite the expression

4 f^{6} - 30 = 0

Move the constant to the right-hand side and change its sign

4 f^{6} = 0 + 30

Removing 0 doesn't change the value,so remove it from the expression

4 f^{6} = 30

Divide both sides

\frac{4 f ^{6}}{4} = \frac{30}{4}

Divide the numbers

f^{6} = \frac{30}{4}

Cancel out the common factor 2

f^{6} = \frac{15}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

f = \pm 6 \frac{15}{2}

Simplify the expression

More Steps

f = \pm \frac{6 480}{2}

Separate the equation into 2 possible cases

f = \frac{6 480}{2} f = - \frac{6 480}{2}

Determine the test intervals using the critical values

f < - \frac{6 480}{2} - \frac{6 480}{2} < f < \frac{6 480}{2} f > \frac{6 480}{2}

Choose a value form each interval

f_{1} = - 2 f_{2} = 0 f_{3} = 2

To determine if f < - \frac{6 480}{2} is the solution to the inequality,test if the chosen value f = - 2 satisfies the initial inequality

More Steps

f < - \frac{6 480}{2} is not a solution f_{2} = 0 f_{3} = 2

To determine if - \frac{6 480}{2} < f < \frac{6 480}{2} is the solution to the inequality,test if the chosen value f = 0 satisfies the initial inequality

More Steps

f < - \frac{6 480}{2} is not a solution - \frac{6 480}{2} < f < \frac{6 480}{2} is the solution f_{3} = 2

To determine if f > \frac{6 480}{2} is the solution to the inequality,test if the chosen value f = 2 satisfies the initial inequality

More Steps

f < - \frac{6 480}{2} is not a solution - \frac{6 480}{2} < f < \frac{6 480}{2} is the solution f > \frac{6 480}{2} is not a solution

Solution

- \frac{6 480}{2} < f < \frac{6 480}{2}

Alternative Form

f \in (- \frac{6 480}{2}, \frac{6 480}{2})

Show Solution