Giải:
a) \(\dfrac{5x-2}{3}< x+1\)
\(\Leftrightarrow5x-2< 3\left(x+1\right)\)
\(\Leftrightarrow5x-2< 3x+3\)
\(\Leftrightarrow5x-3x< 3+2\)
\(\Leftrightarrow2x< 5\)
\(\Leftrightarrow x< \dfrac{5}{2}\)
Vậy ...
b) \(\dfrac{x-1}{4-1}>\dfrac{x+1}{3+8}\)
\(\Leftrightarrow\dfrac{x-1}{3}>\dfrac{x+1}{11}\)
\(\Leftrightarrow\dfrac{11\left(x-1\right)}{33}>\dfrac{3\left(x+1\right)}{33}\)
\(\Leftrightarrow11\left(x-1\right)>3\left(x+1\right)\)
\(\Leftrightarrow11x-11>3x+3\)
\(\Leftrightarrow11x-3x>3+11\)
\(\Leftrightarrow8x>14\)
\(\Leftrightarrow x>\dfrac{14}{8}=\dfrac{7}{4}\)
Vậy ...
a) \(\dfrac{5x-2}{3}< x+1\)
\(\Leftrightarrow\dfrac{5x-2-3x-3}{3}< 0\)
\(\Leftrightarrow2x-5< 0\) (vì 3>0)
\(\Leftrightarrow x< \dfrac{5}{2}\)
Vậy tập nghiệm của pt là \(x< \dfrac{5}{2}\)
b) \(\dfrac{x-1}{4}-1>\dfrac{x+1}{3}+8\)
\(\Leftrightarrow\dfrac{3\left(x-1\right)-12-4\left(x+1\right)-96}{12}>0\)
\(\Leftrightarrow3x-3-12-4x-4-96>0\left(do12>0\right)\)
\(\Leftrightarrow-x-115>0\)
\(\Leftrightarrow x< 115\)
Vậy tập nghiệm của pt là x<115