a, \(\dfrac{2x-3}{-5}>\dfrac{x-2}{-3}\)
<=> \(\dfrac{2x-3}{-5}.-15< \dfrac{x-2}{-3}.-15\)
<=> 3(2x - 3) < 5(x - 2)
<=> 6x - 9 < 5x - 10
<=> x < -1 S = {x|x<-1}
b, \(\dfrac{x-2}{6}-\dfrac{x-1}{3}\le\dfrac{x}{2}\)
<=> \(\dfrac{x-2}{6}-\dfrac{2x-2}{6}\le\dfrac{3x}{6}\)
<=> x - 2 - 2x + 2 \(\le\) 3x
<=> -x\(\le\) 3x
<=> 2x \(\le\) 0
<=> x \(\le\) 0 S = {x|x\(\le\)0}
c,\(2+\dfrac{3\left(x+1\right)}{3}< 3-\dfrac{x-1}{4}\)
<=> 2 + x + 1 < 3 - \(\dfrac{x-1}{4}\)
<=> 12 + x < 12 - x + 1
<=> 2x < 1
<=> x < \(\dfrac{1}{2}\) S = {x|x<\(\dfrac{1}{2}\)}
d,\(5+\dfrac{x+4}{5}< x-\dfrac{x-2}{2}+\dfrac{x+3}{3}\)
<=> \(\dfrac{150}{30}+\dfrac{6x+24}{30}< \dfrac{30x}{30}-\dfrac{15x-30}{30}+\dfrac{10x+30}{30}\)
<=> 150 + 6x + 24 < 30x - 15x + 30 + 10x + 30
<=> 114 < 19x
<=> x > 6 S = {x|x>6}
