What is 5x^3+7x^2>= 58x+24 ?

The solution to 5x^3+7x^2>= 58x+24 is -4 = 3

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5x^3+7x^2>= 58x+24

5 x^{3} + 7 x^{2} \geq 58 x + 24

- 4 \leq x \leq - \frac{2}{5} or x \geq 3

Interval Notation

[- 4, - \frac{2}{5}] \cup [3, \infty)

Decimal Notation

- 4 \leq x \leq - 0.4 or x \geq 3

Solution steps

5 x^{3} + 7 x^{2} \geq 58 x + 24

Rewrite in standard form

5 x^{3} + 7 x^{2} - 24 - 58 x \geq 0

Factor

5 x^{3} + 7 x^{2} - 24 - 58 x : (x - 3) (5 x + 2) (x + 4)

(x - 3) (5 x + 2) (x + 4) \geq 0

Identify the intervals

- 4 \leq x \leq - \frac{2}{5} or x \geq 3

13 x + 25 \leq - 1

4 x + 21 < 9

0.66 > 13.2

9 - (- 3)

\frac{1}{2 m ^{- 4}}

What is 5x^3+7x^2>= 58x+24 ?
The solution to 5x^3+7x^2>= 58x+24 is -4<= x<=-2/5 \lor x>= 3