What is (x-3)^2(21-3x)>0 ?

The solution to (x-3)^2(21-3x)>0 is x<3\lor 3<x<7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(x-3)^2(21-3x)>0

(x - 3)^{2} (21 - 3 x) > 0

x < 3 or 3 < x < 7

Interval Notation

(- \infty, 3) \cup (3, 7)

Solution steps

(x - 3)^{2} (21 - 3 x) > 0

Rewrite in standard form

- x^{3} + 13 x^{2} - 51 x + 63 > 0

Factor

- x^{3} + 13 x^{2} - 51 x + 63 : - (x - 3)^{2} (x - 7)

- (x - 3)^{2} (x - 7) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3)^{2} (x - 7)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3)^{2} (x - 7) < 0

Identify the intervals

x < 3 or 3 < x < 7

r^{2} = 3

4 x - x^{2} = - 6 x

34

\frac{5}{8} - \frac{3}{4} t = \frac{7}{8}

x^{2} - \frac{1}{2} x + \frac{2}{3}