A/ Theo đề ta có \(\frac{x}{2}-\frac{x-5}{10}\) không âm
\(\Rightarrow\frac{x}{2}-\frac{x-5}{10}\ge0\)
\(\Rightarrow\frac{5x}{10}-\frac{x-5}{10}\ge0\)
\(\Rightarrow\frac{5x-x+5}{10}\ge0\)
\(\Rightarrow\frac{4x+5}{10}\ge0\)
\(\Rightarrow4x+5\ge0\)
\(\Rightarrow4x\ge-5\)
\(\Rightarrow x\ge-\frac{5}{4}\)
\(\Rightarrow S=\left\{x\in R;x\ge-\frac{5}{4}\right\}\)
B/ theo đề ta có \(\frac{2x-3}{8}-\frac{x-5}{12}\) không dương
\(\Rightarrow\frac{2x-3}{8}-\frac{x-5}{12}\le0\)
\(\Rightarrow\frac{3\left(2x-3\right)}{24}-\frac{2\left(x-5\right)}{24}\le0\)
\(\Rightarrow\frac{6x-9}{24}-\frac{2x-10}{24}\le0\)
\(\Rightarrow\frac{6x-9-2x+10}{24}\le0\)
\(\Rightarrow\frac{4x-1}{24}\le0\)
\(\Rightarrow4x-1\le0\)
\(\Rightarrow4x\le1\)
\(\Rightarrow x\le\frac{1}{4}\)
\(\Rightarrow S=\left\{x\in R;x\le\frac{1}{4}\right\}\)
