-1\; ;\; \; ODZ:\; 1+2x>0,\; x>-\frac{1}{2}\\\\log_{0,5}(1+2x)>log_{0,5}(0,5)^{-1}\\\\1+2x<(0,5)^{-1}\\\\1+2x<2\\\\2x<1\\\\x<\frac{1}{2}\\\\Otvet:\; \; x\in (-\frac{1}{2},\frac{1}{2})." alt="1)\; log_{0,5}(1+2x) >-1\; ;\; \; ODZ:\; 1+2x>0,\; x>-\frac{1}{2}\\\\log_{0,5}(1+2x)>log_{0,5}(0,5)^{-1}\\\\1+2x<(0,5)^{-1}\\\\1+2x<2\\\\2x<1\\\\x<\frac{1}{2}\\\\Otvet:\; \; x\in (-\frac{1}{2},\frac{1}{2})." align="absmiddle" class="latex-formula">
0,\; x>-\frac{3}{5},\; x>-0,6\\\\log_{\frac{1}{7}}(5x+3) \geq log_{\frac{1}{7}}(\frac{1}{7})^{-\frac{1}{2}}\\\\5x+3 \leq (\frac{1}{7})^{-\frac{1}{2}}\; ;\; \; (\frac{1}{7})^{-\frac{1}{2}}=7^{\frac{1}{2}}=\sqrt7\\\\5x+3 \leq \sqrt7\\\\5x \leq \sqrt7-3\\\\x \leq \frac{\sqrt7-3}{5}\approx -0,07\\\\Otvet:\; \; x\in (-0,6\; ;\; \frac{\sqrt7-3}{5}\, ]" alt="2)\; log_{\frac{1}{7}}(5x+3) \geq -\frac{1}{2}\; ;\; \; ODZ:\; 5x+3>0,\; x>-\frac{3}{5},\; x>-0,6\\\\log_{\frac{1}{7}}(5x+3) \geq log_{\frac{1}{7}}(\frac{1}{7})^{-\frac{1}{2}}\\\\5x+3 \leq (\frac{1}{7})^{-\frac{1}{2}}\; ;\; \; (\frac{1}{7})^{-\frac{1}{2}}=7^{\frac{1}{2}}=\sqrt7\\\\5x+3 \leq \sqrt7\\\\5x \leq \sqrt7-3\\\\x \leq \frac{\sqrt7-3}{5}\approx -0,07\\\\Otvet:\; \; x\in (-0,6\; ;\; \frac{\sqrt7-3}{5}\, ]" align="absmiddle" class="latex-formula">