Solve x^2-3x^23<x^2-4x^35

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, \frac{9}{20})

Evaluate

x^{2} - 3 x^{2} \times 3 < x^{2} - 4 x^{3} \times 5

Simplify

More Steps

- 8 x^{2} < x^{2} - 4 x^{3} \times 5

Multiply the terms

- 8 x^{2} < x^{2} - 20 x^{3}

Move the expression to the left side

- 8 x^{2} - (x^{2} - 20 x^{3}) < 0

Subtract the terms

More Steps

- 9 x^{2} + 20 x^{3} < 0

Rewrite the expression

- 9 x^{2} + 20 x^{3} = 0

Factor the expression

x^{2} (- 9 + 20 x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 - 9 + 20 x = 0

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

x = 0 - 9 + 20 x = 0

Solve the equation

More Steps

x = 0 x = \frac{9}{20}

Determine the test intervals using the critical values

x < 0 0 < x < \frac{9}{20} x > \frac{9}{20}

Choose a value form each interval

x_{1} = - 1 x_{2} = \frac{9}{40} x_{3} = 1

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{9}{40} x_{3} = 1

To determine if 0 < x < \frac{9}{20} is the solution to the inequality,test if the chosen value x = \frac{9}{40} satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < \frac{9}{20} is the solution x_{3} = 1

To determine if x > \frac{9}{20} 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 < \frac{9}{20} is the solution x > \frac{9}{20} is not a solution

Solution

x \in (- \infty, 0) \cup (0, \frac{9}{20})

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