What is 49x-x^3>= 0 ?

The solution to 49x-x^3>= 0 is x<=-7\lor 0<= x<= 7

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49x-x^3>= 0

49 x - x^{3} \geq 0

x \leq - 7 or 0 \leq x \leq 7

Interval Notation

(- \infty, - 7] \cup [0, 7]

Solution steps

49 x - x^{3} \geq 0

Factor

49 x - x^{3} : - x (x + 7) (x - 7)

- x (x + 7) (x - 7) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x + 7) (x - 7)) (- 1) \leq 0 \cdot (- 1)

Simplify

x (x + 7) (x - 7) \leq 0

Identify the intervals

x \leq - 7 or 0 \leq x \leq 7

- x^{3} + 5 x^{2} - x + 5

2 x + 7 > - 11

b^{2} - 25

x^{2} + 4 x + 2 = 0

3 x^{2} - 20 < 0