Solve -2(x^3)<8 - ScanMath

Evaluate

- 2 x^{3} < 8

Move the expression to the left side

- 2 x^{3} - 8 < 0

Rewrite the expression

- 2 x^{3} - 8 = 0

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

- 2 x^{3} = 0 + 8

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

- 2 x^{3} = 8

Change the signs on both sides of the equation

2 x^{3} = - 8

Divide both sides

\frac{2 x ^{3}}{2} = \frac{- 8}{2}

Divide the numbers

x^{3} = \frac{- 8}{2}

Divide the numbers

More Steps

x^{3} = - 4

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

3 x^{3} = 3 - 4

Calculate

x = 3 - 4

An odd root of a negative radicand is always a negative

x = - 34

Determine the test intervals using the critical values

x < - 34 x > - 34

Choose a value form each interval

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

To determine if x < - 34 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 34 is not a solution x_{2} = - 1

To determine if x > - 34 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 34 is not a solution x > - 34 is the solution

Solution

x > - 34

Alternative Form

x \in (- 34, + \infty)

Solve the inequality