Question

x-35/21 + x-36/20 > x-37/19 + x-38/18

Answer 1

Ta có : \(\frac{x-35}{21}+\frac{x-36}{20}>\frac{x-37}{19}+\frac{x-38}{18}\)(1)

\(\Leftrightarrow\left(\frac{x-35}{21}-1\right)+\left(\frac{x-36}{20}-1\right)\)\(-\left(\frac{x-37}{19}-1\right)-\left(\frac{x-38}{18}-1\right)\)\(>0\)

\(\Leftrightarrow\frac{x-56}{21}+\frac{x-56}{20}-\frac{x-56}{19}-\frac{x-56}{18}\)\(>0\)

\(\Leftrightarrow\left(x-56\right)\left(\frac{1}{21}+\frac{1}{20}-\frac{1}{19}-\frac{1}{18}\right)\)\(>0\)

Vì \(\frac{1}{21}+\frac{1}{20}-\frac{1}{19}-\frac{1}{18}< 0\)

\(\Rightarrow x-56< 0\)\(\Leftrightarrow x< 56\)

Vậy tập nghiệm của BPT(1) là \(S=\left\{x\in R|x< 56\right\}\)