Question

Решите неравенство $frac{5x+8}{4-x} textless 2$

Answer 1

$frac{5x+8}{4-x} textless 2, \ left { {{4-xneq0,} atop {frac{5x+8}{4-x}-2 textless 0;}} right. left { {{xneq4,} atop {frac{5x+8-8+2x}{4-x} textless 0;}} right. left { {{xneq4,} atop {frac{7x}{4-x} textless 0;}} right. left { {{xneq4,} atop {frac{x}{x-4} textgreater 0;}} right. left { {{xneq4,} atop x(x-4) textgreater 0;}} right.$
$left [ { left { {{x textless 0,} atop {x-4 textless 0,}} right. } atop { left { {{x textgreater 0,} atop {x-4 textgreater 0;}} right. }} right. left [ { left { {{x textless 0,} atop {x textless 4,}} right. } atop { left { {{x textgreater 0,} atop {x textgreater 4;}} right. }} right. left [x textless 0, } atop {x textgreater 4; }} right. \ xin(-infty;0)cup(4;+infty).$