What is (x-2x^2)*(x+1/2)<= 0 ?

The solution to (x-2x^2)*(x+1/2) = 1/2

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(x-2x^2)*(x+1/2)<= 0

(x - 2 x^{2}) \cdot (x + \frac{1}{2}) \leq 0

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

Interval Notation

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

Decimal Notation

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

Solution steps

(x - 2 x^{2}) (x + \frac{1}{2}) \leq 0

Rewrite in standard form

- 4 x^{3} + x \leq 0

Factor

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

- x (2 x + 1) (2 x - 1) \leq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (2 x + 1) (2 x - 1)) (- 1) \geq 0 \cdot (- 1)

Simplify

x (2 x + 1) (2 x - 1) \geq 0

Identify the intervals

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

y^{3} - 7 y - 6

3 ∣ 8 r + 9 ∣ - 1 > 2

x^{4} + 7 x^{2} - 8

\frac{3}{2} (1) - 2

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