Solve x(x^5)(x-3)<0

Question

Solve the inequality

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

Evaluate

x \times x^{5} (x - 3) < 0

Multiply

More Steps

x^{6} (x - 3) < 0

Rewrite the expression

x^{6} (x - 3) = 0

Separate the equation into 2 possible cases

x^{6} = 0 x - 3 = 0

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

x = 0 x - 3 = 0

Solve the equation

More Steps

x = 0 x = 3

Determine the test intervals using the critical values

x < 0 0 < x < 3 x > 3

Choose a value form each interval

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

To determine if 0 < 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 < 3 is the solution x_{3} = 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 < 3 is the solution x > 3 is not a solution

Solution

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

Show Solution