What is (15)/x >= x/(15-x) ?

The solution to (15)/x >= x/(15-x) is x 15

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(15)/x >= x/(15-x)

\frac{15}{x} \geq \frac{x}{15 - x}

x \leq - \frac{15 + 15 5}{2} or 0 < x \leq \frac{15 5 - 15}{2} or x > 15

Interval Notation

(- \infty, - \frac{15 + 15 5}{2}] \cup (0, \frac{15 5 - 15}{2}] \cup (15, \infty)

Decimal Notation

x \leq - 24.27050 \dots or 0 < x \leq 9.27050 \dots or x > 15

Solution steps

\frac{15}{x} \geq \frac{x}{15 - x}

Rewrite in standard form

\frac{15 ( - x + 15 ) - x ^{2}}{x ( - x + 15 )} \geq 0

Identify the intervals

x \leq - \frac{15 + 15 5}{2} or 0 < x \leq \frac{15 5 - 15}{2} or x > 15

10 g^{2} + 10 = 29 g

2 - x^{2} = x^{2}

x (x + 1) = 1.5 x^{2}

- 5 x + 4 (2 x + 2) = - 1

3 (1 - 2 x) = \frac{1}{4} (6 x + 9)

What is (15)/x >= x/(15-x) ?
The solution to (15)/x >= x/(15-x) is x<=-(15+15sqrt(5))/2 \lor 0<x<= (15sqrt(5)-15)/2 \lor x>15