\(\dfrac{3\left(x-1\right)}{x+2}< 2\)
\(ĐKXĐ:x+2\ne0\Leftrightarrow x\ne-2\)
\(\dfrac{3\left(x-1\right)}{x+2}< 3\)
\(\Leftrightarrow\dfrac{3x-3}{x+2}< 3\)
\(\Leftrightarrow\dfrac{3x-3}{x+2}-3< 0\)
\(\Leftrightarrow\dfrac{3x-3}{x+2}-\dfrac{3\left(x+2\right)}{1\left(x+2\right)}< 0\)
\(\Leftrightarrow\dfrac{3x-3}{x+2}-\dfrac{3x+6}{x+2}< 0\)
\(\Leftrightarrow\dfrac{3x-3-3x-6}{x+2}< 0\)
\(\Leftrightarrow\dfrac{-9}{x+2}< 0\)
Vì \(-9< 0\)
\(\Rightarrow x+2>0\)
\(\Leftrightarrow x>-2\left(TM\right)\)
Vậy bất phương trình có tập nghiệm là: \(S=\left\{xIx>-2\right\}\)
\(\dfrac{x-2}{2}-\dfrac{2}{3}\ge x-1\)
\(\Leftrightarrow\dfrac{\left(x-2\right)3}{2.3}-\dfrac{2.2}{3.2}\ge\dfrac{\left(x-1\right)6}{1.6}\)
\(\Leftrightarrow3x-6-4\ge6x-6\)
\(\Leftrightarrow3x-6x\ge-6+6+4\)
\(\Leftrightarrow-3x\ge4\)
\(\Leftrightarrow x\le-\dfrac{4}{3}\)
Vậy bất phương trình có tập nghiệm là: \(S=\left\{xIx\le-\dfrac{4}{3}\right\}\)
