Solve | 3x^4 | ≥ 8

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - \frac{4 216}{3}] \cup [\frac{4 216}{3}, + \infty)

Evaluate

3 x^{4} \geq 8

Calculate the absolute value

More Steps

3 x^{4} \geq 8

Move the expression to the left side

3 x^{4} - 8 \geq 0

Rewrite the expression

3 x^{4} - 8 = 0

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

3 x^{4} = 0 + 8

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

3 x^{4} = 8

Divide both sides

\frac{3 x ^{4}}{3} = \frac{8}{3}

Divide the numbers

x^{4} = \frac{8}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{8}{3}

Simplify the expression

More Steps

x = \pm \frac{4 216}{3}

Separate the equation into 2 possible cases

x = \frac{4 216}{3} x = - \frac{4 216}{3}

Determine the test intervals using the critical values

x < - \frac{4 216}{3} - \frac{4 216}{3} < x < \frac{4 216}{3} x > \frac{4 216}{3}

Choose a value form each interval

x_{1} = - 2 x_{2} = 0 x_{3} = 2

To determine if x < - \frac{4 216}{3} is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - \frac{4 216}{3} is the solution x_{2} = 0 x_{3} = 2

To determine if - \frac{4 216}{3} < x < \frac{4 216}{3} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{4 216}{3} is the solution - \frac{4 216}{3} < x < \frac{4 216}{3} is not a solution x_{3} = 2

To determine if x > \frac{4 216}{3} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - \frac{4 216}{3} is the solution - \frac{4 216}{3} < x < \frac{4 216}{3} is not a solution x > \frac{4 216}{3} is the solution

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

x \leq - \frac{4 216}{3} is the solution x \geq \frac{4 216}{3} is the solution

Solution

x \in (- \infty, - \frac{4 216}{3}] \cup [\frac{4 216}{3}, + \infty)

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