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

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x/(x+5)>3x

Solution

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

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

Interval Notation

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

Decimal Notation

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

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

\frac{4}{4 ^{- 3}}

\frac{2}{5 i}

- 3 x - 2 > 1

∣ b - 10 ∣ = ∣ 7 b - 15 ∣

\frac{4}{12} = \frac{x}{5}