Solve 2 x<9x^6 - ScanMath

Question

2 x < 9 x^{6}

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 (\frac{5 54}{3}, + \infty)

Evaluate

2 x < 9 x^{6}

Move the expression to the left side

2 x - 9 x^{6} < 0

Rewrite the expression

2 x - 9 x^{6} = 0

Factor the expression

x (2 - 9 x^{5}) = 0

Separate the equation into 2 possible cases

x = 0 2 - 9 x^{5} = 0

Solve the equation

More Steps

x = 0 x = \frac{5 54}{3}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{5 54}{3} x > \frac{5 54}{3}

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{5 54}{6} 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{5 54}{6} x_{3} = 2

To determine if 0 < x < \frac{5 54}{3} is the solution to the inequality,test if the chosen value x = \frac{5 54}{6} satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{5 54}{3} is not a solution x_{3} = 2

To determine if x > \frac{5 54}{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 < \frac{5 54}{3} is not a solution x > \frac{5 54}{3} is the solution

Solution

x \in (- \infty, 0) \cup (\frac{5 54}{3}, + \infty)

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