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

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x/(x+1)>3x

Solution

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

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

Interval Notation

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

Decimal Notation

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

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

(y + 7)^{2} = 16

5 - \frac{x}{7} = 11

\frac{x + 1}{x - 2} \leq 2

4 x^{2} - 8 x - 21 = 0

\frac{4}{5 + i}