Question

giải bất phương trình sau : (x+2)/89 + (x+5)/86 > (x+8)/83 + (x+11)/80

Answer 1

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

\(\Leftrightarrow\dfrac{x+2}{89}+1+\dfrac{x+5}{86}+1>\dfrac{x+8}{83}+1+\dfrac{x+11}{80}+1\)

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

\(\Leftrightarrow\dfrac{x+91}{89}+\dfrac{x+91}{86}-\dfrac{x+91}{83}-\dfrac{x+91}{80}>0\)

\(\Leftrightarrow\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\right)>0\)

Ta có: \(\dfrac{1}{89}+\dfrac{1}{86}+\dfrac{1}{83}+\dfrac{1}{80}< 0\)

\(\Leftrightarrow x+91< 0\)

\(\Leftrightarrow x< -91\)

Vậy...........