Solve 4x(x^5) 2 (x 1)(x - 6) 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 (6, + \infty)

Evaluate

4 x \times x^{5} \times 2 (x \times 1) (x - 6) \times 2 > 0

Remove the parentheses

4 x \times x^{5} \times 2 x \times 1 \times (x - 6) \times 2 > 0

Multiply the terms

More Steps

16 x^{7} (x - 6) > 0

Rewrite the expression

16 x^{7} (x - 6) = 0

Elimination the left coefficient

x^{7} (x - 6) = 0

Separate the equation into 2 possible cases

x^{7} = 0 x - 6 = 0

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

x = 0 x - 6 = 0

Solve the equation

More Steps

x = 0 x = 6

Determine the test intervals using the critical values

x < 0 0 < x < 6 x > 6

Choose a value form each interval

x_{1} = - 1 x_{2} = 3 x_{3} = 7

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} = 3 x_{3} = 7

To determine if 0 < x < 6 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 < 6 is not a solution x_{3} = 7

To determine if x > 6 is the solution to the inequality,test if the chosen value x = 7 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 6 is not a solution x > 6 is the solution

Solution

x \in (- \infty, 0) \cup (6, + \infty)

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