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Popular >

-x^3+x<= 0

Solution

- x^{3} + x \leq 0

Solution

- 1 \leq x \leq 0 or x \geq 1

+1

Interval Notation

[- 1, 0] \cup [1, \infty)

Solution steps

- x^{3} + x \leq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 1 \leq x \leq 0 or x \geq 1

Popular Examples

((x^2+4)(x-2))/((x-3))<0

\frac{( x ^{2} + 4 ) ( x - 2 )}{( x - 3 )} < 0

(12x)/(x-4)>= (6x)/(x+6)

\frac{12 x}{x - 4} \geq \frac{6 x}{x + 6}

- 2 x^{2} + x - 1 < 0

x^{2} - 2 x < 1

x^{2} - 2 > 2 x + 1

Frequently Asked Questions (FAQ)

What is -x^3+x<= 0 ?
The solution to -x^3+x<= 0 is -1<= x<= 0\lor x>= 1