What is x/(x+5)>= 3x ?

The solution to x/(x+5)>= 3x is x<-5\lor-14/3 <= x<= 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x/(x+5)>= 3x

\frac{x}{x + 5} \geq 3 x

x < - 5 or - \frac{14}{3} \leq x \leq 0

Interval Notation

(- \infty, - 5) \cup [- \frac{14}{3}, 0]

Decimal Notation

x < - 5 or - 4.66666 \dots \leq x \leq 0

Solution steps

\frac{x}{x + 5} \geq 3 x

Rewrite in standard form

\frac{- 3 x ^{2} - 14 x}{x + 5} \geq 0

Factor

\frac{- 3 x ^{2} - 14 x}{x + 5} : \frac{- x ( 3 x + 14 )}{x + 5}

\frac{- x ( 3 x + 14 )}{x + 5} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( 3 x + 14 ) ) ( - 1 )}{x + 5} \leq 0 \cdot (- 1)

Simplify

\frac{x ( 3 x + 14 )}{x + 5} \leq 0

Identify the intervals

x < - 5 or - \frac{14}{3} \leq x \leq 0

\frac{x}{13} \geq 1 - \frac{x}{26}

7 + 8 x - 6 - 6 x = 3

\frac{a}{a - b} + \frac{b}{a + b}

5 x + 34 + 2 x + 76 = 180

- x^{2} - 2 x + 580 = 356