Solve 2x^6>22 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - 611) \cup (611, + \infty)

Evaluate

2 x^{6} > 22

Move the expression to the left side

2 x^{6} - 22 > 0

Rewrite the expression

2 x^{6} - 22 = 0

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

2 x^{6} = 0 + 22

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

2 x^{6} = 22

Divide both sides

\frac{2 x ^{6}}{2} = \frac{22}{2}

Divide the numbers

x^{6} = \frac{22}{2}

Divide the numbers

More Steps

x^{6} = 11

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

x = \pm 611

Separate the equation into 2 possible cases

x = 611 x = - 611

Determine the test intervals using the critical values

x < - 611 - 611 < x < 611 x > 611

Choose a value form each interval

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

To determine if x < - 611 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 611 is the solution x_{2} = 0 x_{3} = 2

To determine if - 611 < x < 611 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 611 is the solution - 611 < x < 611 is not a solution x_{3} = 2

To determine if x > 611 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 611 is the solution - 611 < x < 611 is not a solution x > 611 is the solution

Solution

x \in (- \infty, - 611) \cup (611, + \infty)

Show Solution