What is z/(z-5)>= 2z ?

The solution to z/(z-5)>= 2z is z<= 0\lor 5<z<= 11/2

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z/(z-5)>= 2z

\frac{z}{z - 5} \geq 2 z

z \leq 0 or 5 < z \leq \frac{11}{2}

Interval Notation

(- \infty, 0] \cup (5, \frac{11}{2}]

Decimal Notation

z \leq 0 or 5 < z \leq 5.5

Solution steps

\frac{z}{z - 5} \geq 2 z

Rewrite in standard form

\frac{- 2 z ^{2} + 11 z}{z - 5} \geq 0

Factor

\frac{- 2 z ^{2} + 11 z}{z - 5} : \frac{- z ( 2 z - 11 )}{z - 5}

\frac{- z ( 2 z - 11 )}{z - 5} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - z ( 2 z - 11 ) ) ( - 1 )}{z - 5} \leq 0 \cdot (- 1)

Simplify

\frac{z ( 2 z - 11 )}{z - 5} \leq 0

Identify the intervals

z \leq 0 or 5 < z \leq \frac{11}{2}

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