Question

Решите пожалуйста неравенство.

Answer 1

Метод рационализации.

$log_{x} frac{2x-1}{x+4} geq 0; ; Leftrightarrow ; ; left{begin{array}{c}x textgreater 0; ,; xne 1\frac{2x-1}{x+4} textgreater 0\(x-1)(frac{2x-1}{x+4}-1) geq 0end{array}right \\\left{begin{array}{c}x textgreater 0,; xne 1\xin (-infty ,-4)cup (frac{1}{2},+infty )\(x-1)cdot frac{2x-1-x-4}{x+4} geq 0end{array}right ; ; left{begin{array}{cc}xin (frac{1}{2},1)cup (1,+infty )\frac{(x-1)(x-5)}{x+4} geq 0end{array}right$

$left{begin{array}{cc}xin (frac{1}{2},1)cup (1,+infty )\xin (-4,1, ]cup [, 5,+infty )\end{array}right ; ; Rightarrow ; ; xin (frac{1}{2},1)cup [, 5,+infty )$