Solve -42v^33 < 8v 91

Evaluate

- 42 v^{3} \times 3 < 8 v \times 91

Multiply the terms

- 126 v^{3} < 8 v \times 91

Multiply the terms

- 126 v^{3} < 728 v

Move the expression to the left side

- 126 v^{3} - 728 v < 0

Rewrite the expression

- 126 v^{3} - 728 v = 0

Factor the expression

- 14 v (9 v^{2} + 52) = 0

Divide both sides

v (9 v^{2} + 52) = 0

Separate the equation into 2 possible cases

v = 0 9 v^{2} + 52 = 0

Solve the equation

More Steps

v = 0 v \in / R

Find the union

v = 0

Determine the test intervals using the critical values

v < 0 v > 0

Choose a value form each interval

v_{1} = - 1 v_{2} = 1

To determine if v < 0 is the solution to the inequality,test if the chosen value v = - 1 satisfies the initial inequality

More Steps

v < 0 is not a solution v_{2} = 1

To determine if v > 0 is the solution to the inequality,test if the chosen value v = 1 satisfies the initial inequality

More Steps

v < 0 is not a solution v > 0 is the solution

Solution

v > 0

Alternative Form

v \in (0, + \infty)

Solve the inequality