The solution to 9x>2x^2-18 is -3/2 <x<6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

9x>2x^2-18

Solution

9 x > 2 x^{2} - 18

- \frac{3}{2} < x < 6

Interval Notation

(- \frac{3}{2}, 6)

Decimal Notation

- 1.5 < x < 6

Solution steps

9 x > 2 x^{2} - 18

Rewrite in standard form

9 x + 18 - 2 x^{2} > 0

Factor

9 x + 18 - 2 x^{2} : - (2 x + 3) (x - 6)

- (2 x + 3) (x - 6) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (2 x + 3) (x - 6)) (- 1) < 0 \cdot (- 1)

Simplify

(2 x + 3) (x - 6) < 0

Identify the intervals

- \frac{3}{2} < x < 6

\frac{( t - 1 )}{( t - 2 )} > 0

(x^{2} - 2 x) (2 x - 2) - 92 x - 2 x^{3} - 2 x < 0

2 x^{2} + 5 > 4

x^{2} - x - 10 > - 10

x^{2} + 5 x + 12 > 0