Question

giải bất phương trình bậc nhất 1 ẩn :

a) \(\dfrac{2x-3}{x+5}\ge3\) b)\(\dfrac{x-1}{x-3}>1\)

thanks nhìu

Answer 1

a) \(\dfrac{2x-3}{x+5}\ge3\)

\(\Leftrightarrow\dfrac{2x-3}{x+5}-3\ge0\)

\(\Leftrightarrow\dfrac{2x-3-3x-15}{x+5}\ge0\)

\(\Leftrightarrow\dfrac{-x-18}{x+5}\ge0\Leftrightarrow-x-18\ge0\)

\(\Leftrightarrow x\le-18\)

Vậy...................

b) \(\dfrac{x-1}{x-3}>1\)

\(\Leftrightarrow\dfrac{x-1}{x-3}-1>0\)

\(\Leftrightarrow\dfrac{x-1-x+3}{x-3}>0\)

\(\Leftrightarrow\dfrac{2}{x-3}>0\Leftrightarrow x-3>0\Leftrightarrow x>3\)

Vậy..........