Solve -1 < 2n^4 - 5

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for n

n \in (- \infty, - 42) \cup (42, + \infty)

Evaluate

- 1 < 2 n^{4} - 5

Move the expression to the left side

- 1 - (2 n^{4} - 5) < 0

Subtract the terms

More Steps

4 - 2 n^{4} < 0

Rewrite the expression

4 - 2 n^{4} = 0

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

- 2 n^{4} = 0 - 4

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

- 2 n^{4} = - 4

Change the signs on both sides of the equation

2 n^{4} = 4

Divide both sides

\frac{2 n ^{4}}{2} = \frac{4}{2}

Divide the numbers

n^{4} = \frac{4}{2}

Divide the numbers

More Steps

n^{4} = 2

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

n = \pm 42

Separate the equation into 2 possible cases

n = 42 n = - 42

Determine the test intervals using the critical values

n < - 42 - 42 < n < 42 n > 42

Choose a value form each interval

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

To determine if n < - 42 is the solution to the inequality,test if the chosen value n = - 2 satisfies the initial inequality

More Steps

n < - 42 is the solution n_{2} = 0 n_{3} = 2

To determine if - 42 < n < 42 is the solution to the inequality,test if the chosen value n = 0 satisfies the initial inequality

More Steps

n < - 42 is the solution - 42 < n < 42 is not a solution n_{3} = 2

To determine if n > 42 is the solution to the inequality,test if the chosen value n = 2 satisfies the initial inequality

More Steps

n < - 42 is the solution - 42 < n < 42 is not a solution n > 42 is the solution

Solution

n \in (- \infty, - 42) \cup (42, + \infty)

Show Solution