Solve (x^3)(x-1)(x-3)<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, 0) \cup (1, 3)

Evaluate

x^{3} (x - 1) (x - 3) < 0

Rewrite the expression

x^{3} (x - 1) (x - 3) = 0

Separate the equation into 3 possible cases

x^{3} = 0 x - 1 = 0 x - 3 = 0

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

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

Solve the equation

More Steps

x = 0 x = 1 x - 3 = 0

Solve the equation

More Steps

x = 0 x = 1 x = 3

Determine the test intervals using the critical values

x < 0 0 < x < 1 1 < x < 3 x > 3

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{1}{2} x_{3} = 2 x_{4} = 4

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 the solution x_{2} = \frac{1}{2} x_{3} = 2 x_{4} = 4

To determine if 0 < x < 1 is the solution to the inequality,test if the chosen value x = \frac{1}{2} satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 1 is not a solution x_{3} = 2 x_{4} = 4

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

More Steps

x < 0 is the solution 0 < x < 1 is not a solution 1 < 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 < 0 is the solution 0 < x < 1 is not a solution 1 < x < 3 is the solution x > 3 is not a solution

Solution

x \in (- \infty, 0) \cup (1, 3)

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