Solve |3v^6|<9 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for v

- 63 < v < 63

Alternative Form

v \in (- 63, 63)

Evaluate

3 v^{6} < 9

Calculate the absolute value

More Steps

3 v^{6} < 9

Move the expression to the left side

3 v^{6} - 9 < 0

Rewrite the expression

3 v^{6} - 9 = 0

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

3 v^{6} = 0 + 9

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

3 v^{6} = 9

Divide both sides

\frac{3 v ^{6}}{3} = \frac{9}{3}

Divide the numbers

v^{6} = \frac{9}{3}

Divide the numbers

More Steps

v^{6} = 3

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

v = \pm 63

Separate the equation into 2 possible cases

v = 63 v = - 63

Determine the test intervals using the critical values

v < - 63 - 63 < v < 63 v > 63

Choose a value form each interval

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

To determine if v < - 63 is the solution to the inequality,test if the chosen value v = - 2 satisfies the initial inequality

More Steps

v < - 63 is not a solution v_{2} = 0 v_{3} = 2

To determine if - 63 < v < 63 is the solution to the inequality,test if the chosen value v = 0 satisfies the initial inequality

More Steps

v < - 63 is not a solution - 63 < v < 63 is the solution v_{3} = 2

To determine if v > 63 is the solution to the inequality,test if the chosen value v = 2 satisfies the initial inequality

More Steps

v < - 63 is not a solution - 63 < v < 63 is the solution v > 63 is not a solution

Solution

- 63 < v < 63

Alternative Form

v \in (- 63, 63)

Show Solution