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

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

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x/(x-5)>= 3x

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

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

Interval Notation

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

Decimal Notation

x \leq 0 or 5 < x \leq 5.33333 \dots

Solution steps

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

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

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

\frac{z}{- 12} = 5

- 3 x + 3 = - 3 (1 + x)

- 5 ∣ 6 a + 2 ∣ = - 15

24 m^{2} - 31 m - 15

x^{2} + 6 x - 4 = 0