What is 100x-x^3>= 0 ?

The solution to 100x-x^3>= 0 is x<=-10\lor 0<= x<= 10

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100x-x^3>= 0

100 x - x^{3} \geq 0

x \leq - 10 or 0 \leq x \leq 10

Interval Notation

(- \infty, - 10] \cup [0, 10]

Solution steps

100 x - x^{3} \geq 0

Factor

100 x - x^{3} : - x (x + 10) (x - 10)

- x (x + 10) (x - 10) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x + 10) (x - 10)) (- 1) \leq 0 \cdot (- 1)

Simplify

x (x + 10) (x - 10) \leq 0

Identify the intervals

x \leq - 10 or 0 \leq x \leq 10

- ∣ 1 + x ∣ + ∣ 1 - x ∣ = 2

9 - x \geq 10

4 ∣ x - 1 ∣ + 2 = 10

4 x^{2} - 3 x - 2 = 0

3 n + 5 n^{2} = 0