Solve 2x^2-5x-1<11

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

- \frac{3}{2} < x < 4

Alternative Form

x \in (- \frac{3}{2}, 4)

Evaluate

2 x^{2} - 5 x - 1 < 11

Move the expression to the left side

2 x^{2} - 5 x - 1 - 11 < 0

Subtract the numbers

2 x^{2} - 5 x - 12 < 0

Rewrite the expression

2 x^{2} - 5 x - 12 = 0

Factor the expression

More Steps

(x - 4) (2 x + 3) = 0

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

x - 4 = 0 2 x + 3 = 0

Solve the equation for x

More Steps

x = 4 2 x + 3 = 0

Solve the equation for x

More Steps

x = 4 x = - \frac{3}{2}

Determine the test intervals using the critical values

x < - \frac{3}{2} - \frac{3}{2} < x < 4 x > 4

Choose a value form each interval

x_{1} = - 3 x_{2} = 1 x_{3} = 5

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

More Steps

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

To determine if - \frac{3}{2} < x < 4 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < - \frac{3}{2} is not a solution - \frac{3}{2} < x < 4 is the solution x_{3} = 5

To determine if x > 4 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < - \frac{3}{2} is not a solution - \frac{3}{2} < x < 4 is the solution x > 4 is not a solution

Solution

- \frac{3}{2} < x < 4

Alternative Form

x \in (- \frac{3}{2}, 4)

Show Solution