What is -8x^3-30x^2<18x ?

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-8x^3-30x^2<18x

- 8 x^{3} - 30 x^{2} < 18 x

- 3 < x < - \frac{3}{4} or x > 0

Interval Notation

(- 3, - \frac{3}{4}) \cup (0, \infty)

Decimal Notation

- 3 < x < - 0.75 or x > 0

Solution steps

- 8 x^{3} - 30 x^{2} < 18 x

Rewrite in standard form

- 4 x^{3} - 15 x^{2} - 9 x < 0

Factor

- 4 x^{3} - 15 x^{2} - 9 x : - x (4 x + 3) (x + 3)

- x (4 x + 3) (x + 3) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (4 x + 3) (x + 3)) (- 1) > 0 \cdot (- 1)

Simplify

x (4 x + 3) (x + 3) > 0

Identify the intervals

- 3 < x < - \frac{3}{4} or x > 0

4. 8^{2}

3 x^{2} - 18 x - 21 = 0

2 \cdot (3 - x) = 3 \cdot (4 - 3 x) - 6

8 x + 4 = 6 x - 10

\frac{5}{10}