Cong ca hai ve cua bdt voi 2 roi chuyen ve la ra
a) \(\dfrac{x-2}{6}+\dfrac{x-3}{5}< \dfrac{x-4}{4}+\dfrac{x-1}{7}\)
\(\Leftrightarrow\) \(\dfrac{5\left(x-2\right)}{30}+\dfrac{6\left(x-3\right)}{30}< \dfrac{7\left(x-4\right)}{28}+\dfrac{4\left(x-1\right)}{28}\)
\(\Leftrightarrow\) \(\dfrac{11x-28}{30}< \dfrac{11x-31}{28}\)
\(\Leftrightarrow28\left(11-x\right)< 30\left(11x-32\right)\)
\(\Leftrightarrow-22< -176\)
\(\Leftrightarrow x>8\)
b) \(\dfrac{x+2}{7}+\dfrac{x+4}{5}< \dfrac{x+6}{3}+\dfrac{x+1}{8}\)
\(\Leftrightarrow\) \(\dfrac{12x+24}{35}< \dfrac{11x+51}{24}\)
\(\Leftrightarrow\) \(24\left(12x+38\right)< 35\left(11x+51\right)\)
\(\Leftrightarrow-97x< 873\)
\(\Leftrightarrow x>-9\)
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