Solve -2x^2 - 13x - 15 > 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- 5 < x < - \frac{3}{2}

Alternative Form

x \in (- 5, - \frac{3}{2})

Evaluate

- 2 x^{2} - 13 x - 15 > 0

Rewrite the expression

- 2 x^{2} - 13 x - 15 = 0

Factor the expression

More Steps

- (x + 5) (2 x + 3) = 0

Divide the terms

(x + 5) (2 x + 3) = 0

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

x + 5 = 0 2 x + 3 = 0

Solve the equation for x

More Steps

x = - 5 2 x + 3 = 0

Solve the equation for x

More Steps

x = - 5 x = - \frac{3}{2}

Determine the test intervals using the critical values

x < - 5 - 5 < x < - \frac{3}{2} x > - \frac{3}{2}

Choose a value form each interval

x_{1} = - 6 x_{2} = - 3 x_{3} = - 1

To determine if x < - 5 is the solution to the inequality,test if the chosen value x = - 6 satisfies the initial inequality

More Steps

x < - 5 is not a solution x_{2} = - 3 x_{3} = - 1

To determine if - 5 < x < - \frac{3}{2} is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 5 is not a solution - 5 < x < - \frac{3}{2} is the solution x_{3} = - 1

To determine if x > - \frac{3}{2} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 5 is not a solution - 5 < x < - \frac{3}{2} is the solution x > - \frac{3}{2} is not a solution

Solution

- 5 < x < - \frac{3}{2}

Alternative Form

x \in (- 5, - \frac{3}{2})

Show Solution