Solve -8x^3 <_ 19

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > - \frac{3 9}{2}

Alternative Form

x \in (- \frac{3 9}{2}, + \infty)

Evaluate

- 8 x^{3} < 9

Move the expression to the left side

- 8 x^{3} - 9 < 0

Rewrite the expression

- 8 x^{3} - 9 = 0

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

- 8 x^{3} = 0 + 9

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

- 8 x^{3} = 9

Change the signs on both sides of the equation

8 x^{3} = - 9

Divide both sides

\frac{8 x ^{3}}{8} = \frac{- 9}{8}

Divide the numbers

x^{3} = \frac{- 9}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{9}{8}

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

3 x^{3} = 3 - \frac{9}{8}

Calculate

x = 3 - \frac{9}{8}

Simplify the root

More Steps

x = - \frac{3 9}{2}

Determine the test intervals using the critical values

x < - \frac{3 9}{2} x > - \frac{3 9}{2}

Choose a value form each interval

x_{1} = - 2 x_{2} = 0

To determine if x < - \frac{3 9}{2} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{3 9}{2} is not a solution x_{2} = 0

To determine if x > - \frac{3 9}{2} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{3 9}{2} is not a solution x > - \frac{3 9}{2} is the solution

Solution

x > - \frac{3 9}{2}

Alternative Form

x \in (- \frac{3 9}{2}, + \infty)

Show Solution