Solve -x^33≥4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \leq - \frac{3 36}{3}

Alternative Form

x \in (- \infty, - \frac{3 36}{3}]

Evaluate

- x^{3} \times 3 \geq 4

Use the commutative property to reorder the terms

- 3 x^{3} \geq 4

Move the expression to the left side

- 3 x^{3} - 4 \geq 0

Rewrite the expression

- 3 x^{3} - 4 = 0

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

- 3 x^{3} = 0 + 4

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

- 3 x^{3} = 4

Change the signs on both sides of the equation

3 x^{3} = - 4

Divide both sides

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

Divide the numbers

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

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

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

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

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

Calculate

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

Simplify the root

More Steps

x = - \frac{3 36}{3}

Determine the test intervals using the critical values

x < - \frac{3 36}{3} x > - \frac{3 36}{3}

Choose a value form each interval

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

To determine if x < - \frac{3 36}{3} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{3 36}{3} is the solution x_{2} = 0

To determine if x > - \frac{3 36}{3} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{3 36}{3} is the solution x > - \frac{3 36}{3} is not a solution

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

x \leq - \frac{3 36}{3} is the solution

Solution

x \leq - \frac{3 36}{3}

Alternative Form

x \in (- \infty, - \frac{3 36}{3}]

Show Solution