*\(\dfrac{x-3}{4}-\dfrac{x-1}{5}< 2\)
\(\dfrac{5\left(x-3\right)-4\left(x-1\right)}{20}< 2\)
\(\dfrac{5x-15-4x+4}{20}< 2\)
\(\dfrac{x-11}{20}< 2\)
\(x-11< 40\)
\(x< 51\)
* \(\left(x-5\right)^2-x\left(x-2\right)\le4\)
\(x^2-10x+25-x^2+2x\le4\)
\(-8x+25\le4\)
\(-8x\le-21\)
\(x\ge2,625\)
\(\le\)
\(\left(x-5\right)^2-x\left(x-2\right)\le4\)
\(\Leftrightarrow x^2-10x+25-x^2+2x-4\le0\)
\(\Leftrightarrow-8x+21\le0\)
\(\Leftrightarrow x\ge\dfrac{21}{8}\)
Vậy BPT có nghiệm \(x\ge\dfrac{21}{8}\)
\(\dfrac{x-3}{4}-\dfrac{x-1}{5}< 2\)
\(\Leftrightarrow\dfrac{5\left(x-3\right)}{20}-\dfrac{4\left(x-1\right)}{20}< 2\)
\(\Leftrightarrow5x-15-4x+4-2< 0\)
\(\Leftrightarrow x-13< 0\)
\(\Leftrightarrow x< 13\)
Vậy BPT có nghiệm \(x< 13\)
\(3-\dfrac{x-4}{2}>x-3\)
\(\Leftrightarrow\dfrac{3.2}{2}-\dfrac{x-4}{2}>\dfrac{2x}{2}-\dfrac{3.2}{2}\)
\(\Leftrightarrow6-x+4>2x-6\)
\(\Leftrightarrow6-x+4-2x+6>0\)
\(\Leftrightarrow-3x+16>0\)
\(\Leftrightarrow x< \dfrac{16}{3}\)
Vậy BPT có nghiệm \(x< \dfrac{16}{3}\)
*\(3-\dfrac{x-4}{2}>x-3\)
\(\dfrac{6}{2}-\dfrac{x-4}{2}>\dfrac{2\left(x-3\right)}{2}\)
\(6-x+4>2x-6\)
\(-3x>-16\)
\(x< \dfrac{16}{3}\)