[latex]log_{ \frac{1}{7} } (5x+3) \geq - \frac{1}{2} [/latex]

[latex]\log_{\tfrac{1}{7}}(5x+3)\geq-\dfrac{1}{2}\\ D:5x+3\ \textgreater \ 0\\ D:5x\ \textgreater \ -3\\ D:x\ \textgreater \ -\dfrac{3}{5}\\\\ \log_{\tfrac{1}{7}}(5x+3)\geq-\dfrac{1}{2}\\ \log_{\tfrac{1}{7}}(5x+3)\geq\log_{\tfrac{1}{7}}\sqrt7\\ 5x+3\leq\sqrt7\\ 5x\leq-3+\sqrt7\\ x\leq\dfrac{-3+\sqrt7}{5}\\ x\leq-\dfrac{3-\sqrt7}{5}\\\\ x\leq-\dfrac{3-\sqrt7}{5} \wedge x\ \textgreater \ -\dfrac{3}{5}\\ \boxed{x\in\left(-\dfrac{3}{5},-\dfrac{3-\sqrt7}{5}\right)} [/latex]