Solve -65y 19 < -2y^41

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

0 < y < \frac{3 4940}{2}

Alternative Form

y \in (0, \frac{3 4940}{2})

Evaluate

- 65 y \times 19 < - 2 y^{4} \times 1

Multiply the terms

- 1235 y < - 2 y^{4} \times 1

Multiply the terms

- 1235 y < - 2 y^{4}

Move the expression to the left side

- 1235 y - (- 2 y^{4}) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 1235 y + 2 y^{4} < 0

Rewrite the expression

- 1235 y + 2 y^{4} = 0

Factor the expression

y (- 1235 + 2 y^{3}) = 0

Separate the equation into 2 possible cases

y = 0 - 1235 + 2 y^{3} = 0

Solve the equation

More Steps

y = 0 y = \frac{3 4940}{2}

Determine the test intervals using the critical values

y < 0 0 < y < \frac{3 4940}{2} y > \frac{3 4940}{2}

Choose a value form each interval

y_{1} = - 1 y_{2} = 4 y_{3} = 10

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

More Steps

y < 0 is not a solution y_{2} = 4 y_{3} = 10

To determine if 0 < y < \frac{3 4940}{2} is the solution to the inequality,test if the chosen value y = 4 satisfies the initial inequality

More Steps

y < 0 is not a solution 0 < y < \frac{3 4940}{2} is the solution y_{3} = 10

To determine if y > \frac{3 4940}{2} is the solution to the inequality,test if the chosen value y = 10 satisfies the initial inequality

More Steps

y < 0 is not a solution 0 < y < \frac{3 4940}{2} is the solution y > \frac{3 4940}{2} is not a solution

Solution

0 < y < \frac{3 4940}{2}

Alternative Form

y \in (0, \frac{3 4940}{2})

Show Solution