Solve -3|2z^4| 5>-1

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for z

- \frac{4 27000}{30} < z < \frac{4 27000}{30}

Alternative Form

z \in (- \frac{4 27000}{30}, \frac{4 27000}{30})

Evaluate

- 3 2 z^{4} \times 5 > - 1

Simplify

More Steps

- 30 z^{4} > - 1

Move the expression to the left side

- 30 z^{4} - (- 1) > 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 30 z^{4} + 1 > 0

Rewrite the expression

- 30 z^{4} + 1 = 0

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

- 30 z^{4} = 0 - 1

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

- 30 z^{4} = - 1

Change the signs on both sides of the equation

30 z^{4} = 1

Divide both sides

\frac{30 z ^{4}}{30} = \frac{1}{30}

Divide the numbers

z^{4} = \frac{1}{30}

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

z = \pm 4 \frac{1}{30}

Simplify the expression

More Steps

z = \pm \frac{4 27000}{30}

Separate the equation into 2 possible cases

z = \frac{4 27000}{30} z = - \frac{4 27000}{30}

Determine the test intervals using the critical values

z < - \frac{4 27000}{30} - \frac{4 27000}{30} < z < \frac{4 27000}{30} z > \frac{4 27000}{30}

Choose a value form each interval

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

To determine if z < - \frac{4 27000}{30} is the solution to the inequality,test if the chosen value z = - 1 satisfies the initial inequality

More Steps

z < - \frac{4 27000}{30} is not a solution z_{2} = 0 z_{3} = 1

To determine if - \frac{4 27000}{30} < z < \frac{4 27000}{30} is the solution to the inequality,test if the chosen value z = 0 satisfies the initial inequality

More Steps

z < - \frac{4 27000}{30} is not a solution - \frac{4 27000}{30} < z < \frac{4 27000}{30} is the solution z_{3} = 1

To determine if z > \frac{4 27000}{30} is the solution to the inequality,test if the chosen value z = 1 satisfies the initial inequality

More Steps

z < - \frac{4 27000}{30} is not a solution - \frac{4 27000}{30} < z < \frac{4 27000}{30} is the solution z > \frac{4 27000}{30} is not a solution

Solution

- \frac{4 27000}{30} < z < \frac{4 27000}{30}

Alternative Form

z \in (- \frac{4 27000}{30}, \frac{4 27000}{30})

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