The solution to x/(x-5)>3x is x<0\lor 5<x< 16/3

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x/(x-5)>3x

Solution

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

x < 0 or 5 < x < \frac{16}{3}

Interval Notation

(- \infty, 0) \cup (5, \frac{16}{3})

Decimal Notation

x < 0 or 5 < x < 5.33333 \dots

Solution steps

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

Rewrite in standard form

\frac{- 3 x ^{2} + 16 x}{x - 5} > 0

Factor

\frac{- 3 x ^{2} + 16 x}{x - 5} : \frac{- x ( 3 x - 16 )}{x - 5}

\frac{- x ( 3 x - 16 )}{x - 5} > 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - x ( 3 x - 16 ) ) ( - 1 )}{x - 5} < 0 \cdot (- 1)

Simplify

\frac{x ( 3 x - 16 )}{x - 5} < 0

Identify the intervals

x < 0 or 5 < x < \frac{16}{3}

12 x^{2} y^{3} + 9 x^{3} - 6 x^{4} y

∣ 2 x + 4 ∣ = - 6

- \frac{3}{2 ^{2}}

2 x + 5 = 3 x + 6

3 x^{2} - 4 x - 3 = 0