3(x+10) / x+10+3x+x < 3,6

Odpowiedź :

[tex]\frac{3(x+10)}{x+10+3x+x}<3,6\\\\\frac{3(x+10)}{5x+10}<3,6\\\\\frac{3(x+10)}{5(x+2)} < 3,6\\\\x+2 \neq 0\\x\neq -2\\D = R\setminus\{-2\}\\\\\frac{3(x+10)}{5(x+2)}-3,6<0\\\\\frac{3(x+10)}{5(x+2)}-\frac{3,6\cdot5(x+2)}{5(x+2)}<0\\\\\frac{3(x+10)-18(x+2)}{5(x+2)}<0[/tex]

[tex]\frac{3[(x+10)-6(x+2)]}{5(x+2)} < 0 \ \ /\cdot\frac{5}{3}\\\\\frac{x+10-6x-12}{x+2} < 0\\\\\frac{-5x-2}{x+2} < 0 \ \ /\cdot(-1)\\\\\frac{5x+2}{x+2} > 0\\\\(5x+2)(x+2) > 0\\\\x = -\frac{2}{5} = -0,4 \ \ \vee \ x = -2 \ \notin D\\\\x \in (-\infty;-2) \ \cup \ (-0,4;+\infty)[/tex]