Solve 2 (x - 1)(3 - x)(x - 2)2 > 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, 1) \cup (2, 3)

Evaluate

2 (x - 1) (3 - x) (x - 2) \times 2 > 0

Multiply the terms

4 (x - 1) (3 - x) (x - 2) > 0

Rewrite the expression

4 (x - 1) (3 - x) (x - 2) = 0

Elimination the left coefficient

(x - 1) (3 - x) (x - 2) = 0

Separate the equation into 3 possible cases

x - 1 = 0 3 - x = 0 x - 2 = 0

Solve the equation

More Steps

x = 1 3 - x = 0 x - 2 = 0

Solve the equation

More Steps

x = 1 x = 3 x - 2 = 0

Solve the equation

More Steps

x = 1 x = 3 x = 2

Determine the test intervals using the critical values

x < 1 1 < x < 2 2 < x < 3 x > 3

Choose a value form each interval

x_{1} = 0 x_{2} = \frac{3}{2} x_{3} = \frac{5}{2} x_{4} = 4

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

More Steps

x < 1 is the solution x_{2} = \frac{3}{2} x_{3} = \frac{5}{2} x_{4} = 4

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

More Steps

x < 1 is the solution 1 < x < 2 is not a solution x_{3} = \frac{5}{2} x_{4} = 4

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

More Steps

x < 1 is the solution 1 < x < 2 is not a solution 2 < x < 3 is the solution x_{4} = 4

To determine if x > 3 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 1 is the solution 1 < x < 2 is not a solution 2 < x < 3 is the solution x > 3 is not a solution

Solution

x \in (- \infty, 1) \cup (2, 3)

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