Решите уравнение 4/х= - |x|

$\frac{4}{x}=-\left|x\right|\\ D(f): x\neq 0\ ==\ \textgreater \ x\in\left(-\infty;0\right)\cup\left(0;+\infty\right);\\ 1) x\ \textless \ 0:\\ \frac{4}{x}=-\left(-x\right);\\ \frac4x=x;\\ x^2=4;\\ x=\pm2\cup x\ \textless \ 0==\ \textgreater \ x=-2;\\ 2) x\ \textgreater \ 0:\\ \frac{4}{x}=-\left(x\right);\\ \frac4x=-x;\\ x^2=-4;\\ x=\varnothing;\\$

Ответ: х=-2