Solve r^6/10>1 - ScanMath

Evaluate

\frac{r ^{6}}{10} > 1

Multiply both sides of the inequality by 10

\frac{r ^{6}}{10} \times 10 > 1 \times 10

Multiply the terms

r^{6} > 1 \times 10

Multiply the terms

r^{6} > 10

Move the expression to the left side

r^{6} - 10 > 0

Rewrite the expression

r^{6} - 10 = 0

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

r^{6} = 0 + 10

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

r^{6} = 10

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

r = \pm 610

Separate the equation into 2 possible cases

r = 610 r = - 610

Determine the test intervals using the critical values

r < - 610 - 610 < r < 610 r > 610

Choose a value form each interval

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

To determine if r < - 610 is the solution to the inequality,test if the chosen value r = - 2 satisfies the initial inequality

More Steps

r < - 610 is the solution r_{2} = 0 r_{3} = 2

To determine if - 610 < r < 610 is the solution to the inequality,test if the chosen value r = 0 satisfies the initial inequality

More Steps

r < - 610 is the solution - 610 < r < 610 is not a solution r_{3} = 2

To determine if r > 610 is the solution to the inequality,test if the chosen value r = 2 satisfies the initial inequality

More Steps

r < - 610 is the solution - 610 < r < 610 is not a solution r > 610 is the solution

Solution

r \in (- \infty, - 610) \cup (610, + \infty)

Solve the inequality