Solve 2(x 7)^2(x-8)(x-12)<0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

8 < x < 12

Alternative Form

x \in (8, 12)

Evaluate

2 (x \times 7)^{2} (x - 8) (x - 12) < 0

Simplify

More Steps

98 x^{2} (x - 8) (x - 12) < 0

Rewrite the expression

98 x^{2} (x - 8) (x - 12) = 0

Elimination the left coefficient

x^{2} (x - 8) (x - 12) = 0

Separate the equation into 3 possible cases

x^{2} = 0 x - 8 = 0 x - 12 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 8 = 0 x - 12 = 0

Solve the equation

More Steps

x = 0 x = 8 x - 12 = 0

Solve the equation

More Steps

x = 0 x = 8 x = 12

Determine the test intervals using the critical values

x < 0 0 < x < 8 8 < x < 12 x > 12

Choose a value form each interval

x_{1} = - 1 x_{2} = 4 x_{3} = 10 x_{4} = 13

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} = 4 x_{3} = 10 x_{4} = 13

To determine if 0 < x < 8 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 8 is not a solution x_{3} = 10 x_{4} = 13

To determine if 8 < x < 12 is the solution to the inequality,test if the chosen value x = 10 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 8 is not a solution 8 < x < 12 is the solution x_{4} = 13

To determine if x > 12 is the solution to the inequality,test if the chosen value x = 13 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 8 is not a solution 8 < x < 12 is the solution x > 12 is not a solution

Solution

8 < x < 12

Alternative Form

x \in (8, 12)

Show Solution