Solve (x-4)(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, 0) \cup (0, 4)

Evaluate

(x - 4) (x^{2})^{2} < 0

Simplify

More Steps

x^{4} (x - 4) < 0

Rewrite the expression

x^{4} (x - 4) = 0

Separate the equation into 2 possible cases

x^{4} = 0 x - 4 = 0

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

x = 0 x - 4 = 0

Solve the equation

More Steps

x = 0 x = 4

Determine the test intervals using the critical values

x < 0 0 < x < 4 x > 4

Choose a value form each interval

x_{1} = - 1 x_{2} = 2 x_{3} = 5

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} = 5

To determine if 0 < x < 4 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 < 4 is the solution x_{3} = 5

To determine if x > 4 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 4 is the solution x > 4 is not a solution

Solution

x \in (- \infty, 0) \cup (0, 4)

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