Solve -4(x^3) - 8 <12

Evaluate

- 4 x^{3} - 8 < 12

Move the expression to the left side

- 4 x^{3} - 8 - 12 < 0

Subtract the numbers

- 4 x^{3} - 20 < 0

Rewrite the expression

- 4 x^{3} - 20 = 0

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

- 4 x^{3} = 0 + 20

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

- 4 x^{3} = 20

Change the signs on both sides of the equation

4 x^{3} = - 20

Divide both sides

\frac{4 x ^{3}}{4} = \frac{- 20}{4}

Divide the numbers

x^{3} = \frac{- 20}{4}

Divide the numbers

More Steps

x^{3} = - 5

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - 5

Calculate

x = 3 - 5

An odd root of a negative radicand is always a negative

x = - 35

Determine the test intervals using the critical values

x < - 35 x > - 35

Choose a value form each interval

x_{1} = - 3 x_{2} = - 1

To determine if x < - 35 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 35 is not a solution x_{2} = - 1

To determine if x > - 35 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 35 is not a solution x > - 35 is the solution

Solution

x > - 35

Alternative Form

x \in (- 35, + \infty)

Solve the inequality