تدرب وحل التمرينات

حل المتباينات التالية في R باستعمال خواص المتباينات على الأعداد الحقيقية:

$7(y+3)<9-\sqrt[3]{-27}$

$7y<-9\Rightarrow y<\frac{-9}{7}$

$\frac{1}{7}(\mathrm{t}-\frac{1}{8})+\frac{1}{7}\mathrm{t}\ge -\frac{6}{7}$

$2t\ge \frac{-47}{8}\Rightarrow t\ge \frac{-47}{16}$

$\frac{x}{5}\le 4(\frac{1}{\sqrt{36}}-2x)$

$123x\le 10\Rightarrow x\le \frac{10}{123}$

$8(h+3)>12(1-h)$

$20\mathrm{h}>-12\Rightarrow \mathrm{h}>-\frac{3}{5}$

$5(z-\sqrt{3})<7(1-\sqrt{3})$

$2\mathrm{z}<7-2\sqrt{5}\Rightarrow \mathrm{z}<\frac{7-2\sqrt{5}}{2}$

$\frac{1}{6}m-\sqrt[3]{-27}-\frac{2}{3}m\le |-9|$

$-3m\le 36\Rightarrow m\ge -12$

$14\mathrm{k}-\sqrt[3]{-64}\ge 7(\mathrm{k}-1)$

$7\mathrm{k}\ge -11\Rightarrow \mathrm{k}\ge -\frac{11}{7}$

$\frac{-8}{3}(\frac{6}{8}x+\frac{3}{4})>0$

$-2x>2\Rightarrow x<-1$

$9(3+y)<6(y-4)$

$2y<-17\Rightarrow y<\frac{-17}{2}$

$\frac{-2n}{7}\ge \frac{3}{5}+n$

$-21\ge 45\mathrm{n}\Rightarrow \mathrm{n}\le \frac{-7}{15}$

$\frac{1}{6}(z-\sqrt{3})\le \frac{1}{6}(\sqrt{3}-z)$

$2z\le \frac{4}{\sqrt{5}}\Rightarrow z\le \frac{2}{\sqrt{5}}$

$\frac{h}{4}+\frac{2}{3}<\frac{h}{3}+\frac{4}{3}$

$-4<4h-3h\Rightarrow h>-4$

$\frac{8}{\sqrt[3]{-125}}-2x>\frac{2}{5}-x$

$-10>5x\Rightarrow x<-2$

$\frac{1}{9}(y+6)\ge \frac{1}{6}(\sqrt{6}-y)$

$5y<3\sqrt{6}-12\Rightarrow y<\frac{3\sqrt{6}-12}{5}$