$\text{a)}$  

$2-\frac{x+3}{3}<\frac{2x-3}{2}\mid \cdot 6$  

$12-2\left(x+3\right)<3\left(2x-3\right)$  

$12-2x-6<6x-9$  

$6-2x<6x-9\mid -6x-6$  

$-8x<-15\mid :\left(-8\right)$  

$x>\frac{15}{8}$  

$x>1\frac{7}{8}$         

---

$\text{b)}$  

$\frac{2-x}{2}-\frac{2x-1}{3}\le 1-x\mid \cdot 6$  

$3\left(2-x\right)-2\left(2x-1\right)\le 6-6x$  

$6-3x-4x+2\le 6-6x$  

$8-7x\le 6-6x\mid +6x-8$  

$-x\le -2\mid :\left(-1\right)$  

$x\ge 2$  

---

$\text{c)}$  

$\frac{x+4}{12}+1\ge \frac{x}{6}-\frac{3-x}{4}\mid \cdot 12$  

$x+4+12\ge 2x-3\left(3-x\right)$  

$x+16\ge 2x-9+3x$  

$x+16\ge 5x-9\mid -5x-16$  

$-4x\ge -25\mid :\left(-4\right)$  

$x\le \frac{25}{4}$  

$x\le 6\frac{1}{4}$

---

$\text{d)}$  

$\frac{3x+1}{4}-\frac{6-2x}{5}>-\frac{1}{20}-\frac{x-1}{2}\mid \cdot 20$  

$5\left(3x+1\right)-4\left(6-2x\right)>-1-10\left(x-1\right)$  

$15x+5-24+8x>-1-10x+10$  

$23x-19>-10x+9\mid +10x+19$  

$33x>28\mid :33$  

$x>\frac{28}{33}$  

---

$\text{e)}$  

$-\frac{1}{6}x-\frac{2x-5}{4}\ge 3-\frac{8x-3}{3}\mid \cdot 12$  

$-2x-3\left(2x-5\right)\ge 36-4\left(8x-3\right)$  

$-2x-6x+15\ge 36-32x+12$  

$-8x+15\ge -32x+48\mid +32x-15$  

$24x\ge 33\mid :24$  

$x\ge \frac{33}{24}$  

$x\ge \frac{11}{8}$  

$x\ge 1\frac{3}{8}$  

---

$\text{f)}$  

$\frac{x-1}{3}-\frac{2x-1}{6}<\frac{1}{2}-\frac{x-3}{5}\mid \cdot 30$  

$10\left(x-1\right)-5\left(2x-1\right)<15-6\left(x-3\right)$  

$10x-10-10x+5<15-6x+18$  

$-5<-6x+33\mid +6x+5$  

$6x<38\mid :6$  

$x<\frac{38}{6}$  

$x<\frac{19}{3}$  

$x<6\frac{1}{3}$