Question

Giải bất phương trình:

\(\dfrac{x+2}{89}+\dfrac{x+5}{86}>\dfrac{x+8}{83}+\dfrac{x+11}{80}\)

Answer 1

\(\dfrac{x+2}{89}+\dfrac{x+5}{86}>\dfrac{x+8}{83}+\dfrac{x+11}{80}\)

\(\Leftrightarrow\dfrac{x+91}{89}+\dfrac{x+91}{86}>\dfrac{x+91}{83}+\dfrac{x+91}{80}\)

\(\Leftrightarrow\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}\right)>\left(x+91\right)\left(\dfrac{1}{83}+\dfrac{1}{80}\right)\)

Mà \(\dfrac{1}{89}+\dfrac{1}{86}< \dfrac{1}{83}+\dfrac{1}{80}\)

Nên \(x+91< 0\Leftrightarrow x< -91\)