Solve -4x^22x>8x-4

Evaluate

- 4 x^{2} \times 2 x > 8 x - 4

Multiply

More Steps

- 8 x^{3} > 8 x - 4

Move the expression to the left side

- 8 x^{3} - (8 x - 4) > 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

- 8 x^{3} - 8 x + 4 > 0

Rewrite the expression

- 8 x^{3} - 8 x + 4 = 0

Factor the expression

- 4 (2 x^{3} + 2 x - 1) = 0

Divide both sides

2 x^{3} + 2 x - 1 = 0

Calculate

x \approx 0.423854

Determine the test intervals using the critical values

x < 0.423854 x > 0.423854

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < 0.423854 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0.423854 is the solution x_{2} = 1

To determine if x > 0.423854 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0.423854 is the solution x > 0.423854 is not a solution

Solution

x < 0.423854

Alternative Form

x \in (- \infty, 0.423854)

Solve the inequality