Question

2x−15/ 2 ≤ 5 /3 (2−x )

Answer 1

Respuesta:

Espero entiendas ;)

$x<2\quad \mathrm{or}\quad \frac{57-\sqrt{849}}{12}\le \:x\le \frac{57+\sqrt{849}}{12}$

Explicación paso a paso:

pasos

$\frac{2x-15}{2}\le \frac{5}{3\left(2-x\right)}$

$\frac{-6x^2+57x-100}{-x+2}\le \:0$

$\frac{-\left(x-\frac{57+\sqrt{849}}{12}\right)\left(x-\frac{57-\sqrt{849}}{12}\right)}{-x+2}\le \:0$

$\mathrm{Multiplicar\:ambos\:lados\:por\:}-1\mathrm{\:\left(invertir\:la\:desigualdad\right)}$

$\frac{\left(-\left(x-\frac{57+\sqrt{849}}{12}\right)\left(x-\frac{57-\sqrt{849}}{12}\right)\right)\left(-1\right)}{-x+2}\ge \:0\cdot \left(-1\right)$

$\mathrm{Simplificar}$

$\frac{\left(x-\frac{57+\sqrt{849}}{12}\right)\left(x-\frac{57-\sqrt{849}}{12}\right)}{-x+2}\ge \:0$

$x<2\quad \mathrm{or}\quad \frac{57-\sqrt{849}}{12}\le \:x\le \frac{57+\sqrt{849}}{12}$