Solve (5x - x)*( x^6 ) > 20

Evaluate

(5 x - x) x^{6} > 20

Simplify

More Steps

4 x^{7} > 20

Move the expression to the left side

4 x^{7} - 20 > 0

Rewrite the expression

4 x^{7} - 20 = 0

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

4 x^{7} = 0 + 20

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

4 x^{7} = 20

Divide both sides

\frac{4 x ^{7}}{4} = \frac{20}{4}

Divide the numbers

x^{7} = \frac{20}{4}

Divide the numbers

More Steps

x^{7} = 5

Take the 7 -th root on both sides of the equation

7 x^{7} = 75

Calculate

x = 75

Determine the test intervals using the critical values

x < 75 x > 75

Choose a value form each interval

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

To determine if x < 75 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < 75 is not a solution x_{2} = 2

To determine if x > 75 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 75 is not a solution x > 75 is the solution

Solution

x > 75

Alternative Form

x \in (75, + \infty)

Solve the inequality