What is x^3(6x^2+x)>= 2x^3 ?

The solution to x^3(6x^2+x)>= 2x^3 is -2/3 = 1/2

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x^3(6x^2+x)>= 2x^3

x^{3} (6 x^{2} + x) \geq 2 x^{3}

- \frac{2}{3} \leq x \leq 0 or x \geq \frac{1}{2}

Interval Notation

[- \frac{2}{3}, 0] \cup [\frac{1}{2}, \infty)

Decimal Notation

- 0.66666 \dots \leq x \leq 0 or x \geq 0.5

Solution steps

x^{3} (6 x^{2} + x) \geq 2 x^{3}

Rewrite in standard form

6 x^{5} + x^{4} - 2 x^{3} \geq 0

Factor

6 x^{5} + x^{4} - 2 x^{3} : x^{3} (2 x - 1) (3 x + 2)

x^{3} (2 x - 1) (3 x + 2) \geq 0

Identify the intervals

- \frac{2}{3} \leq x \leq 0 or x \geq \frac{1}{2}

12 (5 + 2 y) = 4 y - (5 - 9 y)

5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

x m + y m + x n + y n

- 9 \cdot - 36

25 x^{2} - 4 = 0

What is x^3(6x^2+x)>= 2x^3 ?
The solution to x^3(6x^2+x)>= 2x^3 is -2/3 <= x<= 0\lor x>= 1/2