Solve -9x^3 ≤48

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \geq - \frac{2 3 18}{3}

Alternative Form

x \in [- \frac{2 3 18}{3}, + \infty)

Evaluate

- 9 x^{3} \leq 48

Move the expression to the left side

- 9 x^{3} - 48 \leq 0

Rewrite the expression

- 9 x^{3} - 48 = 0

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

- 9 x^{3} = 0 + 48

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

- 9 x^{3} = 48

Change the signs on both sides of the equation

9 x^{3} = - 48

Divide both sides

\frac{9 x ^{3}}{9} = \frac{- 48}{9}

Divide the numbers

x^{3} = \frac{- 48}{9}

Divide the numbers

More Steps

x^{3} = - \frac{16}{3}

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

3 x^{3} = 3 - \frac{16}{3}

Calculate

x = 3 - \frac{16}{3}

Simplify the root

More Steps

x = - \frac{2 3 18}{3}

Determine the test intervals using the critical values

x < - \frac{2 3 18}{3} x > - \frac{2 3 18}{3}

Choose a value form each interval

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

To determine if x < - \frac{2 3 18}{3} is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - \frac{2 3 18}{3} is not a solution x_{2} = - 1

To determine if x > - \frac{2 3 18}{3} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - \frac{2 3 18}{3} is not a solution x > - \frac{2 3 18}{3} is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \geq - \frac{2 3 18}{3} is the solution

Solution

x \geq - \frac{2 3 18}{3}

Alternative Form

x \in [- \frac{2 3 18}{3}, + \infty)

Show Solution