0\\ log_{0,5}x=-log_2x\\ log_2\frac{1}{x} =-log_2x\\ log_2x=a\\\\ \frac{a}{2-a} \leq 2-a\\ \frac{a}{2-a} -(2-a)\leq 0\\ \frac{a-4+4a-a^2}{2-a} \leq 0\\ \frac{5a-4-a^2}{2-a}\leq 0\\ \frac{(1-a)(a-4)}{2-a} \leq 0\\ ----[1]+++++(2)----[4]+++++\\ log_2x\leq 1\\ x\leq 2\\ 20\\ log_{0,5}x=-log_2x\\ log_2\frac{1}{x} =-log_2x\\ log_2x=a\\\\ \frac{a}{2-a} \leq 2-a\\ \frac{a}{2-a} -(2-a)\leq 0\\ \frac{a-4+4a-a^2}{2-a} \leq 0\\ \frac{5a-4-a^2}{2-a}\leq 0\\ \frac{(1-a)(a-4)}{2-a} \leq 0\\ ----[1]+++++(2)----[4]+++++\\ log_2x\leq 1\\ x\leq 2\\ 2
2.
1) x ≥ 0
![\frac{1}{1-x} \geq x+1\\ \frac{1-(1-x)(x+1)}{1-x} \geq 0\\ \frac{1-1+x^2}{1-x} \geq 0\\ \frac{x^2}{1-x} \geq 0\\ +++++[0]++++++(1)-------\\ x\in[0;1)](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B1-x%7D+%5Cgeq+x%2B1%5C%5C+%5Cfrac%7B1-%281-x%29%28x%2B1%29%7D%7B1-x%7D+%5Cgeq+0%5C%5C+%5Cfrac%7B1-1%2Bx%5E2%7D%7B1-x%7D+%5Cgeq+0%5C%5C+%5Cfrac%7Bx%5E2%7D%7B1-x%7D+%5Cgeq+0%5C%5C+%2B%2B%2B%2B%2B%5B0%5D%2B%2B%2B%2B%2B%2B%281%29-------%5C%5C+x%5Cin%5B0%3B1%29+ "\frac{1}{1-x} \geq x+1\\ \frac{1-(1-x)(x+1)}{1-x} \geq 0\\ \frac{1-1+x^2}{1-x} \geq 0\\ \frac{x^2}{1-x} \geq 0\\ +++++[0]++++++(1)-------\\ x\in[0;1)")
2) x < 0
![\frac{1}{1+x} \geq x+1\\ \frac{1-(x+1)^2}{1+x} \geq 0\\ \frac{1-1-x^2-2x}{1+x} \geq 0\\ \frac{-x(x+2)}{1+x} \geq 0\\ ++++[-2]-----(-1)++++++[0]------\\ x\in(-\infty;-2]U(-1;0)](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B1%2Bx%7D+%5Cgeq+x%2B1%5C%5C+%5Cfrac%7B1-%28x%2B1%29%5E2%7D%7B1%2Bx%7D+%5Cgeq+0%5C%5C+%5Cfrac%7B1-1-x%5E2-2x%7D%7B1%2Bx%7D+%5Cgeq+0%5C%5C+%5Cfrac%7B-x%28x%2B2%29%7D%7B1%2Bx%7D+%5Cgeq+0%5C%5C+%2B%2B%2B%2B%5B-2%5D-----%28-1%29%2B%2B%2B%2B%2B%2B%5B0%5D------%5C%5C+x%5Cin%28-%5Cinfty%3B-2%5DU%28-1%3B0%29+ "\frac{1}{1+x} \geq x+1\\ \frac{1-(x+1)^2}{1+x} \geq 0\\ \frac{1-1-x^2-2x}{1+x} \geq 0\\ \frac{-x(x+2)}{1+x} \geq 0\\ ++++[-2]-----(-1)++++++[0]------\\ x\in(-\infty;-2]U(-1;0)")
Ответ: x∈(-∞; -2] U (-1; 1)