What is x/(x+1)>= 3x ?

The solution to x/(x+1)>= 3x is x<-1\lor-2/3 <= x<= 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x/(x+1)>= 3x

\frac{x}{x + 1} \geq 3 x

x < - 1 or - \frac{2}{3} \leq x \leq 0

Interval Notation

(- \infty, - 1) \cup [- \frac{2}{3}, 0]

Decimal Notation

x < - 1 or - 0.66666 \dots \leq x \leq 0

Solution steps

\frac{x}{x + 1} \geq 3 x

Rewrite in standard form

\frac{- 3 x ^{2} - 2 x}{x + 1} \geq 0

Factor

\frac{- 3 x ^{2} - 2 x}{x + 1} : \frac{- x ( 3 x + 2 )}{x + 1}

\frac{- x ( 3 x + 2 )}{x + 1} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( 3 x + 2 ) ) ( - 1 )}{x + 1} \leq 0 \cdot (- 1)

Simplify

\frac{x ( 3 x + 2 )}{x + 1} \leq 0

Identify the intervals

x < - 1 or - \frac{2}{3} \leq x \leq 0

\frac{x}{x + 1} \geq 3

1 - y = 5

x^{2} + 9 x - 90

\frac{2 y ^{3} \cdot 3 x y ^{3}}{3 x ^{2} y ^{4}}

63 \cdot 3