√15-4=√15-√16<0</span>
31 -8\sqrt{15}\\ x<\dfrac{31 -8\sqrt{15}}{\sqrt{15}-4}=\dfrac{-8(\sqrt{15}-4)-1}{\sqrt{15}-4}=-8+\dfrac{1}{4-\sqrt{15}}\\ \dfrac1{4-\sqrt{15}}=4+\sqrt{15}\in(7,8)\Longrightarrow \max\limits_{\mathbb Z} x=-8+7=-1" alt="(\sqrt{15}-4)x >31 -8\sqrt{15}\\ x<\dfrac{31 -8\sqrt{15}}{\sqrt{15}-4}=\dfrac{-8(\sqrt{15}-4)-1}{\sqrt{15}-4}=-8+\dfrac{1}{4-\sqrt{15}}\\ \dfrac1{4-\sqrt{15}}=4+\sqrt{15}\in(7,8)\Longrightarrow \max\limits_{\mathbb Z} x=-8+7=-1" align="absmiddle" class="latex-formula">