Solve -6z-4(2z-7)>4z^4-8z

Question

Solve the inequality

- 1.762205 < z < 1.478765

Alternative Form

z \in (- 1.762205, 1.478765)

Evaluate

- 6 z - 4 (2 z - 7) > 4 z^{4} - 8 z

Move the expression to the left side

- 6 z - 4 (2 z - 7) - (4 z^{4} - 8 z) > 0

Subtract the terms

More Steps

- 6 z + 28 - 4 z^{4} > 0

Rewrite the expression

- 6 z + 28 - 4 z^{4} = 0

Factor the expression

- 2 (3 z - 14 + 2 z^{4}) = 0

Divide both sides

3 z - 14 + 2 z^{4} = 0

Calculate

z \approx - 1.762205 z \approx 1.478765

Determine the test intervals using the critical values

z < - 1.762205 - 1.762205 < z < 1.478765 z > 1.478765

Choose a value form each interval

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

To determine if z < - 1.762205 is the solution to the inequality,test if the chosen value z = - 3 satisfies the initial inequality

More Steps

z < - 1.762205 is not a solution z_{2} = 0 z_{3} = 2

To determine if - 1.762205 < z < 1.478765 is the solution to the inequality,test if the chosen value z = 0 satisfies the initial inequality

More Steps

z < - 1.762205 is not a solution - 1.762205 < z < 1.478765 is the solution z_{3} = 2

To determine if z > 1.478765 is the solution to the inequality,test if the chosen value z = 2 satisfies the initial inequality

More Steps

z < - 1.762205 is not a solution - 1.762205 < z < 1.478765 is the solution z > 1.478765 is not a solution

Solution

- 1.762205 < z < 1.478765

Alternative Form

z \in (- 1.762205, 1.478765)

Show Solution