Solve -11y^2-2y 9>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for y

- \frac{18}{11} < y < 0

Alternative Form

y \in (- \frac{18}{11}, 0)

Evaluate

- 11 y^{2} - 2 y \times 9 > 0

Multiply the terms

- 11 y^{2} - 18 y > 0

Rewrite the expression

- 11 y^{2} - 18 y = 0

Factor the expression

More Steps

- y (11 y + 18) = 0

When the product of factors equals 0,at least one factor is 0

- y = 0 11 y + 18 = 0

Solve the equation for y

y = 0 11 y + 18 = 0

Solve the equation for y

More Steps

y = 0 y = - \frac{18}{11}

Determine the test intervals using the critical values

y < - \frac{18}{11} - \frac{18}{11} < y < 0 y > 0

Choose a value form each interval

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

To determine if y < - \frac{18}{11} is the solution to the inequality,test if the chosen value y = - 3 satisfies the initial inequality

More Steps

y < - \frac{18}{11} is not a solution y_{2} = - 1 y_{3} = 1

To determine if - \frac{18}{11} < y < 0 is the solution to the inequality,test if the chosen value y = - 1 satisfies the initial inequality

More Steps

y < - \frac{18}{11} is not a solution - \frac{18}{11} < y < 0 is the solution y_{3} = 1

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 < - \frac{18}{11} is not a solution - \frac{18}{11} < y < 0 is the solution y > 0 is not a solution

Solution

- \frac{18}{11} < y < 0

Alternative Form

y \in (- \frac{18}{11}, 0)

Show Solution