Solve 3x^5>11 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x > \frac{5 891}{3}

Alternative Form

x \in (\frac{5 891}{3}, + \infty)

Evaluate

3 x^{5} > 11

Move the expression to the left side

3 x^{5} - 11 > 0

Rewrite the expression

3 x^{5} - 11 = 0

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

3 x^{5} = 0 + 11

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

3 x^{5} = 11

Divide both sides

\frac{3 x ^{5}}{3} = \frac{11}{3}

Divide the numbers

x^{5} = \frac{11}{3}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{11}{3}

Calculate

x = 5 \frac{11}{3}

Simplify the root

More Steps

x = \frac{5 891}{3}

Determine the test intervals using the critical values

x < \frac{5 891}{3} x > \frac{5 891}{3}

Choose a value form each interval

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

To determine if x < \frac{5 891}{3} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < \frac{5 891}{3} is not a solution x_{2} = 2

To determine if x > \frac{5 891}{3} is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < \frac{5 891}{3} is not a solution x > \frac{5 891}{3} is the solution

Solution

x > \frac{5 891}{3}

Alternative Form

x \in (\frac{5 891}{3}, + \infty)

Show Solution