Solve -13n^4n <= 18

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for n

n \geq - \frac{5 514098}{13}

Alternative Form

n \in [- \frac{5 514098}{13}, + \infty)

Evaluate

- 13 n^{4} \times n \leq 18

Multiply

More Steps

- 13 n^{5} \leq 18

Move the expression to the left side

- 13 n^{5} - 18 \leq 0

Rewrite the expression

- 13 n^{5} - 18 = 0

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

- 13 n^{5} = 0 + 18

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

- 13 n^{5} = 18

Change the signs on both sides of the equation

13 n^{5} = - 18

Divide both sides

\frac{13 n ^{5}}{13} = \frac{- 18}{13}

Divide the numbers

n^{5} = \frac{- 18}{13}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n^{5} = - \frac{18}{13}

Take the 5 -th root on both sides of the equation

5 n^{5} = 5 - \frac{18}{13}

Calculate

n = 5 - \frac{18}{13}

Simplify the root

More Steps

n = - \frac{5 514098}{13}

Determine the test intervals using the critical values

n < - \frac{5 514098}{13} n > - \frac{5 514098}{13}

Choose a value form each interval

n_{1} = - 2 n_{2} = 0

To determine if n < - \frac{5 514098}{13} is the solution to the inequality,test if the chosen value n = - 2 satisfies the initial inequality

More Steps

n < - \frac{5 514098}{13} is not a solution n_{2} = 0

To determine if n > - \frac{5 514098}{13} is the solution to the inequality,test if the chosen value n = 0 satisfies the initial inequality

More Steps

n < - \frac{5 514098}{13} is not a solution n > - \frac{5 514098}{13} is the solution

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

n \geq - \frac{5 514098}{13} is the solution

Solution

n \geq - \frac{5 514098}{13}

Alternative Form

n \in [- \frac{5 514098}{13}, + \infty)

Show Solution