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

Evaluate

(x - 1) x^{2} < 0

Multiply the terms

x^{2} (x - 1) < 0

Rewrite the expression

x^{2} (x - 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 x - 1 = 0

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

x = 0 x - 1 = 0

Solve the equation

More Steps

x = 0 x = 1

Determine the test intervals using the critical values

x < 0 0 < x < 1 x > 1

Choose a value form each interval

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

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

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 the solution x_{3} = 2

To determine if x > 1 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 the solution x > 1 is not a solution

Solution

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

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