Solve x^2 -5x 6 < 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

0 < x < 30

Alternative Form

x \in (0, 30)

Evaluate

x^{2} - 5 x \times 6 < 0

Multiply the terms

x^{2} - 30 x < 0

Rewrite the expression

x^{2} - 30 x = 0

Factor the expression

More Steps

x (x - 30) = 0

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

x = 0 x - 30 = 0

Solve the equation for x

More Steps

x = 0 x = 30

Determine the test intervals using the critical values

x < 0 0 < x < 30 x > 30

Choose a value form each interval

x_{1} = - 1 x_{2} = 15 x_{3} = 31

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

More Steps

x < 0 is not a solution x_{2} = 15 x_{3} = 31

To determine if 0 < x < 30 is the solution to the inequality,test if the chosen value x = 15 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 30 is the solution x_{3} = 31

To determine if x > 30 is the solution to the inequality,test if the chosen value x = 31 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 30 is the solution x > 30 is not a solution

Solution

0 < x < 30

Alternative Form

x \in (0, 30)

Show Solution