Solve 3x(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, 2)

Evaluate

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

Remove the parentheses

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

Multiply the terms

More Steps

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

Rewrite the expression

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 2 = 0

Solve the equation

More Steps

x = 0 x = 2

Determine the test intervals using the critical values

x < 0 0 < x < 2 x > 2

Choose a value form each interval

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

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} = 1 x_{3} = 3

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

More Steps

x < 0 is the solution 0 < x < 2 is the solution x_{3} = 3

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

More Steps

x < 0 is the solution 0 < x < 2 is the solution x > 2 is not a solution

Solution

x \in (- \infty, 0) \cup (0, 2)

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