a)
2 + \frac{x}{2} = \frac{1-x}{3} \ |*6
12+3x=2(1-x) \\ 12+3x=2-2x \\ 3x+2x=2-12 \\ 5x=-10 \ |:5 \\ x=-2
b)
-\frac{x+3}{5}-1=3-\frac{5x}{2} \ |*10
-2(x+3)-10=30-25x
-2x-6-10=30-25x \\ 25x-2x=30+6+10 \\ 23x=46 \\ x=2
c)
\frac{2(x+3)}{9}-4=\frac{2x+3}{6}-x \ |*18 \\ 4(x+3)-72=3(2x+3)-18x \\ 4x+12-72=6x+9-18x \\ 4x-6x+18x=9-12+72 \\ 16x=69\\ x=\frac{69}{16} \\ x=4\frac{5}{16}
d)
-\frac{2x-1}{9}+\frac{4x-5}{15}=x-5 \ |*45 \\ -5(2x-1)+3(4x-5)=45x-225 \\ -10x+5+12x-15=45x-225 \\ 2x-45x=15-5-225 \\ -43x=-215 \ |:(-43) \\ x=5
e)
-\frac{5(x-2)}{2}=5-\frac{3x}{4} \ |*(-4) \\ 10(x-2)=-20+3x \\ 10x-20=-20+3x \\ 10x-3x=-20+20 \\ 7x=0 \ |:7 \\ x=0
f)
1-[\frac{3(x+5)}{2}+\frac{3x}{5}]=-1 \\ 1-\frac{15(x+5)+6x}{10}=-1 \ |*10 \\ 10-(15x+75+6x)=-10 \\ 10-15x-75-6x=-10 \\ -21x=-10-10+75 \\ -21x=55 \ |:(-21) \\ x=-\frac{55}{21} \\ x=-2\frac{13}{21}