$a)$

$\frac{2-x}{5}\le \frac{x+1}{2}\mid \cdot 10$

$2\left(2-x\right)\le 5\left(x+1\right)$

$4-2x\le 5x+5\mid -5x-4$

$-7x\le 1\mid :\left(-7\right)$

$x\ge -\frac{1}{7}$

 

 

$b)$

$\frac{2x-1}{4}\le \frac{2x+1}{3}\mid \cdot 12$

$3\left(2x-1\right)\le 4\left(2x+1\right)$

$6x-3<8x+4\mid -8x+3$

$-2x<7\mid :\left(-2\right)$

$x>-\frac{7}{2}$

 

 

 

 

$c)$

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

$3-3\left(x-1\right)>2\left(x-2\right)$

$3-3x+3>2x-4$

$-3x+6>2x-4\mid -2x-6$

$-5x>-10\mid :\left(-5\right)$

$x<2$

 

 

 

 

$d)$

$\frac{x-2}{2}\le 1-\frac{2x+1}{5}\mid \cdot 10$

$5\left(x-2\right)\le 10-2\left(2x+1\right)$

$5x-10\le 10-4x-2$

$5x-10\le 8-4x\mid +4x+10$

$9x\le 18\mid :9$

$x\le 2$

 

 

 

 

$e)$

$\frac{2x+2}{3}\ge x-\frac{2-x}{5}\mid \cdot 15$

$5\left(2x+2\right)\ge 15x-3\left(2-x\right)$

$10x+10\ge 15x-6+3x$

$10x+10\ge 18x-6\mid -18x-10$

$-8x\ge -16\mid :\left(-8\right)$

$x\le 2$

 

 

 

 

$f)$

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

$12x-3\left(3-x\right)<6-2\left(x+3\right)$

$12x-9+3x<6-2x-6$

$15x-9<-2x\mid +2x+9$

$17x<9\mid :17$

$x<\frac{9}{17}$